Modern  Physics 
Laboratory  Manual 


Projects  and  Problems 

for 

Secondary  Physics 


Prepared  by  the  Physics’  Teachers'  Association 
of  Minneapolis 


A.  VV.  HURD 

North  High 

J.  H.  SANTEE 

North  High 


J.  V.  S.  FISHER 
South  High 


J.  R.  TOYVNE 

East  High 


EARL  SWEET 
Central  High 


H.  J.  ROHDE 

Central  \ High  P 


INDEX 


1.  English  and  Metric  Units  of  Measurement. 

2.  Diagonal  Scale. 

3.  Construction  of  Vernier  Caliper. 

4.  Application  of  Vernier  Caliper. 

5.  Micrometer  Caliper. 

6.  Density  of  a Regular  Solid. 

7.  Principle  of  Moments. 

8.  Center  of  Gravity. 

9.  Liclined  Plane. 

10.  Block  and  Tackle. 

11.  Parallelogram  of  Forces. 

12.  Government  Barometer. 

1 3.  Boyle’s  Law. 

14.  Water  and  Gas  Pressures.  Open  Manometer. 

15.  Archimedes’  Principle. 

16.  Specific  Gravity  of  a Solid  Heavier  Than 

Water. 

7.  Specific  Gravity  of  a Solid  Lighter  Than 
Water. 

Specific  Gravity  of  a Liquid  by  Loss  of  Weight 
Method. 

Specific  Gravity  of  a Liquid  by  Hare's  Method. 
l Hooke’s  Law', 
breaking  Strength  of  Wires, 
jesting  Fixed  Points  of  a Thermometer. 

Viect  of  Pressure  on  Boiling  Point, 
efficient  of  Linear  Expansion. 

Lata  of  Heat  Exchange. 

26.  Spe\  ific  Heat  of  a Metal. 

27.  Dew)  Point  and  Relative  Humidity. 

28.  Heat\  of  Fusion. 

29.  Heatj  of  Vaporization. 

30.  Imaglcs  in  a Plane  Mirror. 


Copyri 


■ight\  92 


921  by  Henry  J.  Rohde,  Earl  Sweet,  J. 
Mail  Address:  A.  W.  Hurd, 


31.  Images  in  a Concave  Mirror. 

32.  Index  of  Refraction. 

33.  Focal  Length  of  a Convex  Lens. 

34.  Images  Formed  by  a Convex  Lens. 

35.  Astronomical  Telescope. 

36.  Erecting  Telescope. 

37.  Vibration  Rate  by  Siren  Disc  Method. 

38.  Vibration  Rate  by  Resonator  Method. 

39.  Velocity  of  Sound  Resonator  Method. 

40.  Law  of  Lengths  of  Vibrating  Strings. 

41.  Law  of  Tension  of  Vibrating  Strings. 

42.  Speed  of  Sound  in  a Metal. 

43.  Magnetic  Fields. 

44.  Theory  of  Magnetism. 

45.  Distribution  of  Magnetism. 

46.  Electroscope. 

47.  Relation  of  Static  to  Current  Electricity. 

48.  Magnetic  Effects  of  an  Electric  Current. 

49.  Electric  Bell  Circuits. 

50.  Cells  in  Series  and  Parallel. 

51.  Relation  of  P.  D.  and  R. 

52.  Law  of  Induced  Currents. 

53.  Testing  of  Fuses. 

54.  Resistance  of  Lamps  in  Series. 

55.  Resistance  of  Lamps  in  Parallel. 

56.  Wheatstone  Bridge. 

. 57.  Electrical  Energy  in  a Circuit. 

58.  Cost  Per  Hour  for  Flatiron,  etc. 

59.  Efficiency  of  an  Electric  Stove,  etc. 

60.  Efficiency  of  a Gas  Burner. 

61.  Telephone. 

62.  Study  of  Motor  and  Dynamo. 

63.  Efficiency  of  Electric  Motor. 

64.  Transformer. 

R.  Towne,  J.  H.  Santee,  J.  V.  S.  Fisher,  A.  W.  Hurd. 
Norih  High  School,  Minneapolis. 


PROBLEM  No.  1 


To  Measure  Carefully  in  English  and  Metric  Units  the  Length  and  Breadth  of  a Sheet  of 

Paper  and  Compare  These  Units. 

Write  the  words,  “top,”  “bottom,”  “right,” 
and  “left,”  on  the  corresponding  edges  of  the 
paper.  Measure  these  edges,  first  in  English 
units  and  then  in  metric  units.  Avoid  using 
the  end  of  the  ruler  and  be  careful  to  place  it 
parallel  with  the  edge  of  the  paper. 

Express  the  English  units  in  terms  of 
inches,  giving  approximately  hundredths  of 
an  inch.  Express  the  metric  units  in  terms 
of  centimeters,  estimating  to  tenths  of  milli- 
meters (hundredths  of  centimeters). 

Record  all  fractions  in  decimals.  Find  the 
number  of  centimeters  in  an  inch.  Compare 
the  “computed”  value  with  the  “accepted” 
value,  as  given  in  your  text-book.  Carry  the 
division  to  the  third  decimal  place. 

From  the  average  results  obtained  for  the 
width  and  length,  compute  the  area  of  the 
sheet  of  paper  in  square  inches  and  also  in 
square  centimeters.  Find  the  number  of 
square  centimeters  in  a square  inch  and  com- 
pare with  the  accepted  equivalent. 

Results : 

1.  Width  in  inches. 

(Top)..  . (Bottom)....  Average 

2.  Width  in  cm. 

(Top) ....  (Bottom) ....  Average 

3.  From  these  averages  determine  the  num- 
ber of  cm.  in  an  inch 

4.  Length  in  inches. 

(Right) (Left) ....  Average.  . . . 

5.  Length  in  cm. 

(Right) (Left)....  Average.... 

6.  From  these  averages,  determine  the 

number  of  centimeters  in  an  inch 

7.  Average  number  of  centimeters  in  an 

inch  (computed)  

8.  Number  of  centimeters  in  an  inch  (ac- 
cepted)   

9.  Difference 

10.  Per  cent  of  error 

Diff. 


accepted=Per  cent  of  error. 


o 

v/U 


100 


11.  Area  in  square  cm 

12.  Area  in  square  inches  

13.  Number  of  square  cm.  in  a square  inch 

(computed)  

I 

14.  Number  of  square  cm.  in  a square  inch 

(accepted)  

15.  Difference 

16.  Per  cent  of  error 

a.  Why  is  it  not  desirable  to  begin  measur- 

ing from  the  end  of  the  rule? 

b.  Give  the  dimension  in  inches  of  the 

famous  French  75  millimeter  gun. 

c.  39.37  inches  equals  100  cm. 

.3937  inches  equals  1 cm. 

1 inch 


.3937 

d.  What  does  the  answer  to  (c)  express? 


PROBLEM  No.  2 


To  Measure  the  Distance  Between  Points  to  Hundredths  of  a Centimeter,  by  Means  of  a 

Diagonal  Scale. 

1.  What  pail  of  an  inch  would  this  be? 

Draw  a diagonal  scale  in  your  note-book 
as  follows:  Construct  eleven  parallel  lines, 
four  centimeters  long  and  two  millimeters 
apart.  Cross  these  lines  by  perpendiculars, 
one  centimeter  apart.  Divide  those  portions 
of  lines  one  and  eleven,  falling  between  the 
last  two  perpendiculars  on  the  right,  into  ten 
equal  parts  each  and  call  the  left  side  zero. 

Now  join  with  a straight  line,  the  point 
marked  no-tenths  on  the  horizontal  line  num- 
bered one  with  the  point  marked  one-tenth 
on  the  horizontal  line  numbered  eleven.  Join 
the  remaining  tenths  by  lines  parallel  to  the 
one  just  drawn.  Notice  that  the  lines  are 
one-tenth  of  a centimeter  farther  to  the 
right  on  line  eleven  than  on  line  one.  Each 
line  passes  over  ten  equal  spaces  in  moving 
one-tenth  to  the  right. 

' 2.  Figure  out  what  part  of  a centimeter  it 
moves  to  the  right  in  crossing  one  space. 

Ask  your  instructor  to  locate  the  points  to 
be  measured. 

Mark  them  with  letters  as  A.  B. 

Adjust  a pair  of  dividers  to  the  exact  dis- 
tance without  touching  the  points  to  the  pa- 
per. Place  the  dividers  on  the  top  horizon- 
tal line  with  the  left  leg  of  the  divider  on 
such  a centimeter  division  that  the  right  leg 
will  fall  in  the  last  centimeter  division  con- 
taining the  diagonal  scale.  From  this,  read 
the  v ’’stance  in  centimeters  and  tenths.  Then 
move  'oth  legs  of  the  dividers  down  the  scale 
until  ti  e right  leg  exactly  strikes  an  inter- 
section. Now  get  the  reading  to  hundredths 
of  a centimeter. 

3.  Could  you  read  the  third  decimal  by  es- 
timating a part  of  one  space?  If  so,  how? 

4.  Would  this  estimate  increase  the  accu- 
racy of  your  measurement?  Why? 

5.  How  may  you  be  sure  that  the  dividers 
have  not  moved  while  you  were  taking  the 
reading? 

Average  several  readings  for  the  final  val- 
ue and  tabulate  all  of  them. 

6.  Why  do  we  measure  things?  Would  it 
not  be  better  to  estimate  such  things  as  mon- 
ey. gas,  electricity  and  land? 

7.  How  does  an  estimate  differ  from  a 
guess  ? 


r 


. 


. 

' 

_ 

•it!  ;»i< 

" 

••  ■ 1 


PROBLEM  No.  3 

To  Make  a Vernier  Caliper. 

Along  the  middle  of  a card  draw  a straight 
line,  AB.  Beginning  at  a point  about  2 cm. 
from  the  left  end,  lay  off  along  AB  a scale  of 
centimeters.  To  do  this,  stand  the  centi- 
meter rule  on  edge,  so  that  one  of  the  centi- 
meter marks  of  the  scale  is  at  the  starting 
point.  Mark  a fine  dot  with  a sharp  pencil 
opposite  each  succeeding  centimeter  mark 
for  about  12  centimeters. 

Be  sure  that  each  dot  is  accurately  in  line 
with  the  mark  on  this  scale  and  through  each 
one  erect  perpendiculars  to  AB. 

Number  them  0.  1,  2,  3,  etc.,  at  their  top. 

On  the  other  side  of  the  line  AB  lay  off  in 
the  same  way  a scale  of  10  divisions,  each  di- 
vision being  9 mm.  long.  This  scale  must 
start  at  the  same  point  (0)  as  the  first  scale. 

The  line  marked  10  on  this  new  scale  will 
then  be  found  to  coincide  with  the  9 line  of 
the  centimeter  scale.  This  new  scale  is  call- 
ed the  vernier. 

About  5 mm.  to  the  left  of  the  zero  divi- 
sion draw  a line,  CD,  perpendicular  to  AB  on 
the  side  having  the  vernier  scale.  With  a 
scissors  cut  along  this  line  and  also  along  AB 
to  the  right.  Cut  the  edges  smooth.  Now 
you  have  a model  vernier  caliper  by  which 
the  diameter  of  a round  object  may  be  meas- 
ured. 

(1)  When  the  jaws  are  closed,  what  is  the 
distance  between  the  1 mark  of  the  vernier 
and  the  1 mark  of  the  scale? 

(2)  How  will  you  know  when  the  jaws  are 
0.1  cm.  apart?  0.1  mm.? 


% 


'••V  . i <:n-/F  ■ <j  ' r.T 


' 

. 


PROBLEM  No.  4 

To  Measure  the  Dimensions  of  a Metal  Cylinder  With  a Vernier  Caliper  and  Determine 
the  Value  of  Pi  From  the  Measurements  Obtained. 

By  the  use  of  a vernier  caliper,  measure- 
ments may  be  made  accurately  to  tenths  of 
a millimeter. 

1.  On  the  caliper,  notice  that  10  equal  divi- 
sions on  the  movable  scale,  which  is  called 
the  vernier,  cover  9 millimeter  divisions  on 
the  fixed  scale. 

2.  By  what  part  of  a scale  unit  (mm.)  does 
each  division  of  the  vernier  differ  from  that 
of  the  fixed  scale? 

The  first  line  on  the  vernier  is  called  the 
zero  line,  or  reading  line.  Place  line  No.  1 
(second  line)  of  the  vernier  exactly  opposite 
line  No.  1 (second  line)  of  the  scale. 

3.  By  what  part  of  a millimeter  are  the 
jaws  separated? 

4.  Explain  how  you  determine  this. 

Place  the  lines  No.  2 of  the  scale  together. 

5.  Now,  what  is  the  distance  between  the 
jays?  Observe  this  distance  when  other 
corresponding  lines  are  opposite. 

To  see  if  you  understand  how  to  read  the 
scale  on  this  caliper,  set  it  at  the  following 
values  and  if  in  doubt,  take  them  to  the  in- 
structor for  verification:  1.6  mm.,  .4  mm., 

16.7  mm. 

Cut  off  a narrow  strip  of  note-book  paper 
and  wran  it  around  the  cylinder  until  it  over- 
laps. Then,  thrust  a sharp  needle  through 
the  overlapping  portion.  Measure  the  dis- 
tance between  these  points  as  accurately  as 
possible.  Repeat  for  three  readings.  Next, 
measure  the  diameter  of  this  cylinder  in 
three  different  places. 

6.  Why  do  you  take  each  measurement 
three  times? 

Using  the  average  values,  compute  the 
value  of  Pi  and  compare  it  with  the  accented 
value  (3.1416).  Determine  the  per  cent  of 
' error.  Put  this  data  in  a convenient  TABU- 
LAR FORM.  Be  sure  to  record  the  number 
of  your  evlinder. 

7.  Read  the  vernier  scale  on  the  barometer 
as  accurately  as  you  can  and  record  this  val- 
ue in  your  report. 


PROBLEM  No.  5 

To  Measure  the  Diameter  of  the  SAMP]  Cylinder  With  a Micrometer  Caliper. 


Caution:  Never  force  the  screw  tight  as 
it  will  injure  the  instrument.  Use  ratchet 
where  provided  and  where  not,  use  extreme 
care. 

The  micrometer  is  a precision  measuring 
instrument,  which  is  used  to  obtain  more  ac- 
curate results  than  can  be  obtained  with  the 
vernier.  On  an  inner  sleeve,  there  is  a longi- 
tudinal scale  of  millimeter  divisions,  while 
on  the  outer  revolving  sleeve,  there  is  a cir- 
cular scale  divided  into  50  equal  parts.  In 
this  instrument,  the  distance  between  the 
threads  of  the  screw  (called  the  pitch)  is 
such  that  it  is  necessary  to  turn  the  revolv- 
ing sleeve  through  two  complete  revolutions 
to  separate  the  jaws  a distance  of  one  milli- 
meter. 

1.  What  distance  will  the  jaws  be  opened 
when  the  outside  sleeve  is  turned  through 
one  of  its  divisions  ? Turn  it  through  one  of 
these  divisions  and  holding  the  caliper  to  a 
strong  light,  notice  the  distance  the  jaws 
have  opened. 

2.  What  distance  is  covered  by  one  com- 
plete turn  of  the  sleeve  ? 

Set  the  micrometer  at  the  following  values 
and  if  in  doubt,  have  the  instructor  verify 
each : 2.20  mm.,  2.02  mm.,  0.22  mm.,  5.36  mm. 

Before  making  a measurement  with  the 
caliper,  it  is  always  necessary  to  take  what 
is  known  as  the  “zero  reading;”  that  is,  to 
determine  whether  or  not  the  zero  line  on 
the  ciicular  scale  is  opposite  the  zero  line  on 
the  longitudinal  scale.  If  they  are  not  oppo- 
site. then  make  a record  of  the  reading, 
which  must  be  added  to,  or  subtracted  from, 
each  reading  made  with  this  particular  cali- 
per. It  is  also  important  that  the  same  pres- 
sure be  exerted  at  the  jaws  for  each  meas- 
urement, otherwise  the  results  will  be  erron- 
eous. To  get  this  even  pressure,  a ratchet 
head  is  sometimes  attached  to  the  instru- 
ment. Where  this  device  is  lacking,  hold 
the  head  of  the  screw  as  loosely  as  possible 
when  setting  the  caliper,  thus  allowing  the 
fingers  to  slip  as  soon  as  contact  is  made  and 
so  avoiding  undue  pressure. 


Measure  the  thickness  of  several  small  ob- 
jects, such  as  a sheet  of  note  book  paper,  the 
diameter  of  your  hair,  etc.  Notice  if  these 
objects  are  of  uniform  dimensions.  Record 
your  results. 

Also  measure  the  diameter  of  the  cylinder 
used  in  Problem  3 and  compare  this  value 
with  the  result  obtained  when  you  used  the 
vernier. 

3 What  degree  of  accuracy  can  be  ex- 
pected of  this  caliper? 

4.  What  degree  can  be  estimated? 

5.  What  is  meant  by  the  pitch  of  a screw  ? 

6.  What  is  the  pitch  numerically  equal  to 
in  this  micrometer? 


PROBLEM  No.  6 


To  Find  the  Density  of  a Regular  Solid,  Whose  Volume  Can  Be  Found  by  Direct  Measui 

ment. 

(mass  or 

The  density  of  a body  is  its  (weight  per 
unit  volume — in  the  metric  system  usually 
expressed  in  grams  per  cubic  centimeter. 

(mass  or 

1.  Given  the  (weight  and  volume,  how  is 
the  density  computed? 

In  this  experiment,  do  as  careful  work  as 
you  can  and  see  how  accurate  a result  you 
can  get.  Be  sure  you  have  a regular  solid 
whose  measurements  may  be  obtained  eas- 
ily. Measure  the  dimensions  with  a 30  cm. 
rule  (use  a pair  of  outside  calipers  with  the 
30  cm.  rule,  if  you  have  them),  a vernier  or 
micrometer  caliper,  getting  readings  in  cen- 
timeters to  at  least  two  decimal  places.  Take 
three  readings  of  each  dimension,  being  care- 
ful to  take  no  two  in  the  same  place.  Com- 
pute the  volume  from  the  average  readings, 
indicating  clearly  the  method  of  computa- 
tion. 

To  find  the  weight,  use  a beam  balance  and 
set  of  weights.  Take  a complete  set  of 
weights  and  try  to  keep  it  intact.  (Do  not 
let  others  borrow  single  weights  from  you 
and  do  not  borrow  them  from  others.  A set 
of  weights  with  missing  weights  is  worthless 
in  itself  for  weighing  purposes.)  In  using 
the  balance,  see  that  the  pointer  is  at  the 
middle  of  the  scale  with  no  weights  on  either 
pan.  Each  balance  has  an  adjustable  nut  to 
use  in  securing  proper  equilibrium  in  the  be- 
ginning. Tf  this  is  not  sufficient,  use  paper. 

After  you  have  secured  the  desired  equilibri- 
um. place  the  object  you  wish  to  weigh  on 
the  left  hand  scale  pan  and  the  largest 
weight  less  than  the  weight  of  the  body  that 
you  find  will  most  nearly  balance  it  on  the 
ri Hit  hand  scale  pan.  Add  weights,  always 
using  the  largest  possible  ones,  working 
down  step  by  step  from  the  larger  to  smaller, 
finally  making  use  of  the  sliding  weight,  if 
your  balance  is  provided  with  one,  until  the 
pointer  again  rests  at  the  middle  of  the  arc. 

The  sum  of  the  weights  plus  the  reading  in- 
dicated by  the  sliding  bob  will  be  the  ap- 
proximate weight  of  the  object.  Follow 
these  directions  unless  otherwise  directed. 


Compute  the  density  as  indicated  in  your  j 
answer  to  (1). 

Make  a neat  complete  tabulation  of  results 
which  will  show  clearly  the  general  method 
of  procedure.  It  should  contain  each  meas- 
urement of  dimensions  to  hundredths  of  cen- 
timeters, averages,  volume  (showing  method 
of  computation),  weight,  density  (showing 
method  of  computation),  and  the  accepted 
value  of  the  density  of  the  substance  used  as 
recorded  in  a table  of  densities. 

2.  Mention  at  least  two  reasons  why  you 
would  not  vouch  for  the  accuracy  of  your 
final  result. 

3.  How  does  the  weight  of  the  substance 
you  used  compare  with  that  of  water? 

4.  Give  reasons  for  your  answer  to  (3). 

5.  If  the  body  you  have  used  in  this  ex- 
periment is  non-porous  and  insoluble  in  water 
and  you  have  a cylindrical  glass  vessel  gradu- 
ated in  cubic  centimeters,  suggest  a method 
for  finding  the  valume  of  the  body,  other 
than  by  measurement  of  its  dimensions. 


PROBLEM  No.  7 


To  Test  the  Principle  of  Moments  and  to  Work  Out  the  Law  of  the  Lever. 

A moment  of  a force  is  defined  as  the  prod- 
uct of  the  force  and  the  perpendicular  dis- 
tance from  the  fulcrum  to  the  line  in  which 
the  force  acts. 

1.  Slip  the  meter  stick  through  the  clamp 
and  fix  the  knife  edge  exactly  at  the  50  cm. 
mark.  If  the  meter  stick  will  not  balance 
horizontally  on  the  knife  edge,  place  a clip 
or  wire  at  such  a position  that  the  meter 
stick  will  balance  and  keep  the  clip  there 
throughout  the  experiment. 

Call  the  fulcrum  F. 

2.  Suspend  by  a loop  of  thread  a 100  gram 
weight  on  the  right  side  of  the  bar  at  a place 
where  it  will  exactly  balance  200  g.  placed 
at  a definite  place  on  the  left. 

Make  a straight  line  diagram  and  record 
values  in  figures  on  the  sketch. 


4 o o k /cL  = /o  c x sd 


Find  the  moment  of  each  force  and,  using 
the  equation  below  the  diagraam,  test  its 
truth. 

3.  Repeat  the  test,  placing  the  weights  at 
other  positions  and  record  the  same  way. 

4.  Suspend  a 50  g.  weight  and  100  g. 
weight  at  different  points  on  the  right  side 
of  the  fulcrum  and  balance  with  the  200 
gram  weight  on  the  left. 

Record  on  a sketch  similar  to  the  first  one. 

5.  Repeat  the  last  trial,  using  the  100 
gram  and  200  gram  weigRts  on  the  right 
side,  balancing  the  500  gram  weight  on  the 
left. 

Make  a diagram  for  each  trial. 

6.  Repeat,  using  an  unknown  weight  such 
as  a lead  cylinder  on  one  side;  a known 
weight  on  the  other.  Form  an  equation,  let- 
ting x equal  the  unknown  weight,  and  solve 
for. 

Verify  by  weighing  on  a beam  balance. 


Questions. 

A.  Which  method  of  weighing  do  you 
consider  more  accurate  and  why? 

B.  A boy  weighing  95  lbs.  is  4 ft.  from 
the  fulcrum  on  a see-saw.  Two  boys  are 
balancing  him  on  the  other  side  of  F,  one 
weighing  60  lbs.  2 ft.  from  F,  the  other 
weighing  70  lbs.  How  far  from  F is  the  last 
boy? 


PROBLEM  No.  8 


To  Prove  That  a Body  Acts  as  if  Its  Weight  Is  Collected  at  Its  Center  of  Gravity. 

Find  the  line  of  the  center  of  gravity  of  a | 
tapering  rod  about  one  meter  long  by  bal- 
ancing it  on  a sharp  edge  support.  Mark  the 
position  after  seeing  that  the  fulcrum  edge 
and  the  edge  of  the  rod  are  perpendicular  to 
each  other.  Hang  a 200  g.  weight  (W)  by 
means  of  a light  thread  10  cm.  from  the 
tapering  end  of  the  rod  and  balance  again. 

Mark  the  position  of  the  fulcrum.  Measure 
and  record  the  distances  from  the  fulcrum 
to  the  weight  (W)  and  from  the  fulcrum  to 
the  center  of  gravity.  Call  these  distances 
dx  and  d2  respectively. 

It  is  evident  that  the  moment  of  the 
weight  (W),  which  is  equal  to  W times  d, 
must  be  balanced  by  the  moment  of  a weight 
on  the  other  side  of  the  fulcrum.  Let  us  as- 
sume that  such  a weight  (X)  is  at  the  cen- 
ter of  gravity.  Then  the  moment  of  such  a 
weight  is  equal  to  X times  d2.  From  the 
principle  of  moments  of  a lever  W times  d, 
equals  X times  d2.  Solving  for  X,  a weight 
at  the  center  of  gravity  is  calculated.  Re- 
peat with  the  weight  (W)  at  20  and  30  cm. 
from  the  end.  Average  the  computed  weight 
at  the  center  of  gravity. 

Weigh  the  rod  and  compare  its  weight 
with  the  computed  weight  at  the  center  of 
gravity.  Tabulate  results  showing  weight 
W,  d1(  d2,  computed  weight  at  center  of 
gravity  X,  average  and  weight  of  rod. 

1.  What  does  this  experiment  prove  con- 
cerning where  the  weight  of  a lever  is  con- 
centrated V 

2.  Which  trial  should  give  the  best  result? 

Why? 

3.  A boy  weighing  120  lbs.  uses  a see-saw 
12  ft.  long,  which  weighs  140  lbs.  and  which 
has  its  center  of  gravity  in  the  middle.  If 
the  boy  sits  1 ft.  from  the  end,  where  is  the 
fulcrum  from  this  end,  in  order  to  produce 
balance  ? 


* 


. 


' 

■ 


PROBLEM  No.  9 


To  Compute  and  to  Compare  the  Efficiency  of  an  Inclined  Plane  at  Different  Angles. 

The  efficiency  of  a machine  is  the  ratio  of 
the  output  to  the  input. 

Set  up  a board  to  be  used  as  an  inclined 
plane  at  about  15  degrees.  Measure  off  some 
convenient  length,  50  or  100  cm.,  along  the 
lower  edge  of  the  plane  from  the  base. 

Measure  height  to  the  bottom  of  board  at  the 
length  taken.  Adjust  the  plane  until  the 
height  to  the  marked  off  length  will  make  a 
15  degree  angle.  Weight  a car;  add  a known 
weight  for  load  in  the  car;  place  this  car  on 
the  inclined  plane  and  attach-  weights  by 
means  of  a cord  passing  over  a pulley.  In 
this  way  determine  the  effort  required  to 
pull  the  car  up  slowly  and  uniformly,  apply- 
ing the  force  parallel  to  the  face  of  the  plane. 

Repeat  with  different  angles,  say  20°  and 
30°. 

Compute  the  input  and  the  output  for  the 
different  grades.  The  work  put  in,  the  in- 
put, is  equal  to  the  product  of  the  effort  and 
the  measured  length.  The  work  accom- 
plished, the  output,  is  equal  to  the  product  of 
the  total  load  and  the  measured  height. 

Compute  the  efficiency  for  each  angle.  Tabu- 
late the  results  showing  weight  of  car,  total 
load,  effort,  length,  height,  input,  output,  ef- 
ficiency. 

1.  What  is  gained  by  using  an  inclined 
plane  ? 

2.  The  efficiency  in  pulling  a 100  ton  train 
up  an  incline,  the  height  of  which  is  2 feet 
for  each  length  of  100  feet,  is  90  %.  How 
much  must  the  engine  pull?  With  no  fric- 
tion, what  would  have  been  the  pull? 


- 

•li.  - o'  '•» 

••  ; • 

. 

• ; 

r> 

: .3 


PROBLEM  No.  10 


To  Find  the  Efficiency  of  a Block  and  Tackle. 

Arrange  any  combination  of  pulleys  you 
may  choose.  Attach  a heavy  weight  to  the 
movable  block.  Put  suitable  weights  on  the 
ends  of  the  free  rope  till  they  just  pull  the 
heavy  weight  up  slowly.  Make  three  trials. 

Count  the  number  of  ropes  that  support 
the  weight.  This  number  is  called  the  Me- 
chanical Advantage. 

1.  If  the  small  weights  move  through  a 
distance  of  60  centimeters,  how  far  does  the 
heavy  weight  move? 

It  is  obvious  that  the  small  weights  do 
work  on  the  large  weight  in  making  it  move 
slowly  upward.  To  find  what  is  called  the 
input,  or  work  expended,  when  the  force  or 
effort  works  through  a certain  distance,  ob- 
tain the  product  of  the  force  and  distance. 

The  output,  or  work  accomplished,  is  found 
similarly  by  obtaining  the  product  of  the 
weight  and  the  distance  it  moves  in  the  same 
operation.  If  there  are  six  strands  of  rope, 
the  force  will  move  through  a distance  six 
times  as  great  as  the  weight. 

Make  a simple  diagram,  indicating  The 
weight  lifted,  the  force  acting  and  actual 
arrangement  of  cord  used. 

2.  How  much  work  will  be  accomplished 
(Output)  under  the  conditions  stated  in  1 ? 

3.  Under  the  same  conditions,  how  much 
work  will  be  expended  (Input)  ? 

4.  Efficiency  being  the  ratio  of  the  work 
accomplished  or  output,  to  the  work  expend- 
ed, or  input,  compute  the  efficiency  of  the 
pulleys. 

Were  the  efficiency  of  the  pulley  100%, 
the  two  quantities  formed  in  (2)  and  (3) 
would  be  equal. 

5.  Why  is  not  efficiency  100%? 

6.  If  the  efficiency  of  the  pulleys  were 
100%,  what  would  be  the  ratio  of  the  weight 
to  the  force  with  six  strands? 

7.  Supposing  the  set  you  have  to  be  strong 
enough  and  the  efficiency  to  be  80%,  how 
much  weight  could  you  lift  with  a force  of 
250  lbs.? 

8.  Is  the  work  obtained  from  a set  of  pul- 
leys greater  or  less  than  the  work  put  in? 

9.  What  is  gained  by  using  a set  of  pul- 
leys? 


• -J 

1 ; i i 

■ 

■ • • 

. 


PROBLEM  No.  11 

To  Find  the  Resultant  of  two  Non-parallel  Forces  and  to  Compare  With  Their  Equilibrant. 


Method  A:  Arrange  the  apparatus  ac- 
cording to  the  diagram* 


Place  the  balances  down  on  the  table,  ad- 
justing the  system  so  that  each  balance  reg- 
isters more  than  half  but  less  than  full  scale. 

If  the  balances  do  not  register  zero  with 
no  tension,  an  allowance  must  be  made  for 
the  amount  of  error.  This  is  called  the  zero 
error. 

Place  a sheet  of  paper  from  notebook  un- 
der the  junction  of  the  cords,  and  transfer 
the  angles  to  the  paper.  This  should  be  done 
without  disturbing  the  set  up.  One  way  is 
by  marking  two  dashes  under  each  cord,  af- 
terward drawing  lines  through  each  pair. 

Read  each  balance  carefully  and  record  the 
value  on  the  line  running  to  that  balance. 
The  paper  may  then  be  removed  and  the  ten- 
sion on  balances  released  by  unfastening  any 
one  of  them. 

Finish  the  experiment  as  follows  using  rul- 
er and  compass  and  a sharp  pointed  pencil. 

Mark  the  junction  of  the  three  straight 
lines  O.  Mark  the  other  ends  A,  B,  C.  Choos- 
ing any  two  of  the  three,  say  OB  and  OC, 
construct  a parallelogram  to  scale  as  follows, 
letting  Yu"  equal  1 ounce: — 

Lay  off  on  the  lines  OB  and  OC  as  many 
units  as  the  reading  of  the  spring  balances 
indicate.  With  each  of  these  points  as  a 
center  and  the  opposite  side  as  a radius,  de- 
scribe arcs  cutting  each  other.  Mark  the 
intersection  F.  Draw  OF  and  measure  it 
carefully  to  scale  of  the  drawing. 


1.  Is  OF  equal  to  OA? 

2.  Is  OF  opposite  OA? 

3.  What  is  the  name  of  OF  relative  to  the 
forces  OB  and  OC? 

4.  What  is  the  name  of  OA  relative  to  the 
forces  OB  and  OC? 

5.  State  in  a single  sentence  two  things 
which  you  have  shown  to  be  true  in  the  ex- 
periment regarding  relation  of  resultant  and 
equilibrant. 


PROBLEM  No.  12 


To  Explain  the  Principle  of  the  Barometer  and  Read  a U.  S.  Government  Barometer,  Hav- 
ing a Vernier  Scale. 

I.  Describe  Torricelli’s  experiment  and  an- 
swer the  following  questions: — 

1.  How  long  a tube  is  used  in  performing 
the  experiment?  Why? 

2.  Why  was  mercury  used  instead  of 
water  ? 

3.  What  kept  the  mercury  supported  in 
the  tube? 

4.  How  is  a barometer  like  a Torricellian 
tube? 

5.  What  does  an  area  of  “low  pressure”  on 
a weather  map  indicate? 

6.  When  the  usual  statement,  e.g.  “the 
pressure  today  is  74.25  cm.,”  is  made,  what  is 
the  interpretation  so  that  it  really  means 
pressure?  (Cm.  are  not  units  of  pressure, 
are  they  ?) 

7.  What  does  the  word  “pressure”  mean 
in  Physics? 

8.  Calculate  the  downward  “force”  of  the 
atmosphere  on  a table  3 meters  long  and  2 
meters  wide,  when  the  barometer  reads 
74.39  cm. 

II.  To  read  the  barometer. 

1.  The  cup  at  the  bottom  must  first  be  ad- 
justed so  that  the  little  ivory  pointer  which 
marks  the  zero  of  the  linear  scale,  just 
touches  the  surface  of  the  mercury  in  the 
cup.  (The  cup  is  adjusted  by  means  of  a 
set  screw  at  the  bottom.  Be  sure  you  see 
the  pointer  before  adjusting  the  set  screw.) 

2.  After  the  cup  is  adjusted  correctly,  no- 
tice the  movable  scale  toward  the  top,  which 
is  adjustable  by  means  of  another  set  screw 
at  the  side.  This  movable  scale  should  be 
adjusted  so  that  its  lower  surface  is  just  I 
tangent  to  the  convex  surface  of  the  mer- 
cury in  the  tube. 

3.  The  reading  can  now  be  obtained  in  cm. 
and  tenths  of  cm.  by  noting  the  reading  on 
the  fixed  scale  opposite  the  bottom  of  the 
movable  scale.  The  purpose  of  the  movable 
scale  is  to  get  a reading  accurate  to  hun- 
dredths of  a cm. 


4.  To  do  this,  note  which  line  on  the  mov- 
able scale  most  nearly  coincides  with  a line 
on  the  fixed  scale.  The  number  of  this  line 
(on  the  movable  scale)  gives  the  number  of 
hundredths  of  cm.  For  example,  suppose 
that  the  reading  opposite  the  bottom  of  the 
movable  scale  is  more  than  74.2  cm.  and  yet 
not  74.3,  i.e.,  between  74.2  cm.  and  74.3  cm. 
Now  on  looking  to  see  what  line  of  the  mov- 
able scale  most  nearly  coincides  with  a line 
on  the  fixed  scale,  suppose  it  to  be  the  sev- 
enth. The  number  of  hundredths  indicated 
is,  therefore,  seven.  The  correct  reading  is 
74.27  cm. 

The  reading  in  inches  to  hundredths  is  ob- 
tained similarly. 

This  form  of  scale  is  called  a vernier  scale. 
It  is  so  made  that  ten  divisions  on  the  mov- 
able scale  is  equal  to  nine  divisions  on  the 
fixed  scale.  By  carefully  studying  the  scale, 
the  truth  of  its  principle  described  above  will 
be  understood. 

III.  Read  the  barometer  as  suggested  in 
both  cm.  and  inches  and  draw  neatly  and 
accurately  a figure  showing  all  of  the  mov- 
able scale  and  enough  of  the  fixed  scale  to 
show  plainly  one  reading,  either  cm.  or 
inches.  This  drawing  will  show  whether 
or  not  you  know  how  to  read  the  scale. 
(Try  it  roughly  on  scratch  paper  first, 
so  as  not  to  spoil  your  page.  It  will  be 
easier  to  make  it  many  times  the  actual 
size.) 

IV.  Read  the  barometer  every  day  for  three 
days  and  neatly  tabulate  readings. 

V.  Why  does  a barometer  read  differently 
on  different  days? 

2.  Why  is  the  cup  at  the  bottom  adjust- 
able? 

3.  What  is  the  effect  of  altitude  on  a ba- 
rometer reading?  Why? 


PROBLEM  No.  13 


To  Verify  Boyle’s  Law. 


Arrange  the  mercury  tube  in  an  upright 
position  (position  1 in  the  diagram),  being 
sure  to  have  the  sealed  end  at  the  top.  Call 
the  end  of  the  mercury  column  next  the  seal- 
ed end  A;  the  opposite  end  of  the  mercury 
column  B : and  the  sealed  end  D. 

With  a meter  stick,  measure  carefully  the 
length  of  the  air  column  AD  in  cms.  As- 
suming the  coss-section  of  the  tube  is  every- 
where the  same,  the  volume  of  the  confined 
air  will  always  be  proportional  to  its  length ; 
meters  of  mercury,  to  which  the  air  V,  is 
subjected.  Call  this  pressure  P,. 

Next  measure  the  length  of  the  mercury 
column  AB  in  cms.  Read  the  barometer  in 
cms.  This  barometric  height  minus  the 
length  AB  is  the  pressure,  measured  in  centi- 
meters of  mercury,  to  which  the  air  VI  is 
subjected.  Call  this  pressure  PI. 

Turn  the  tube  slowly  to  position  II  of  the 
diagram.  Now  measure  the  heights  of  the 
points  A and  B above  the  table  and  subtract 
the  difference  between  these  two  distances 
(representing  the  vertical  height  of  the  mer- 
cury column)  from  the  barometric  reading,  j 
thus  obtaining  P.„  the  pressure  correspond- 
ing to  volume  V... 

Place  the  tube  successively  in  positions 
ITT,  IV  and  V,  calling  the  volumes  V.,  V,, 
etc.  Measure  each  case  the  heights  of  A 
and  B from  the  table  and  compute  the  cor- 
responding pressure  P.,,  P„  etc. 

(Remember  that  the  pressure  on  the  con- 
fined air  is  less  than  the  barometric  pressure 
if  the  open  end  of  the  tube  is  lower  than  the 
closed  end,  and  greater  than  the  barometric 
pressure  if  the  open  end  is  higher  than  the 
closed  end.) 


Record  as  indicated  by  the  instructor. 

1.  What  is  Boyle’s  Law? 

2.  If  the  pressure  of  the  atmosphere  is  15 
lbs.  to  the  square  inch,  how  many  times  the 
capacity  of  an  auto  tire  may  be  pumped  into 
it  when  the  pressure  gauge  indicates  a pres- 
sure of  70  lbs.  per  sq.  inch,  supposing,  of 
course,  that  the  fabric  of  the  tire  does  not 
allow  it  to  expand? 


PROBLEM  No.  14 


A.  To  Find  the  Pressure  of  the  City  Gas;  B.  To  Find  the  Pressuie  of  \oui  Lungs 

Both  by  Means  of  Open  Manometers. 

A.  Arrange  two  open  manometers,  one  con- 
taining water  and  the  other  alcohol,  so  that 
the  gas  pressure  may  force  the  liquids  up 
in  the  long  arm  of  the  manometers.  Turn 
on  the  gas  and  carefully  measure  the 
height  of  the  liquid  in  the  long  tube  above 
that  in  the  short  tube  in  each  manometer 
in  inches.  When  gas  pressure  is  spoken 
of  in  this  country,  it  is  usually  expressed 
in  inches  of  water  that  it  will  hold  up  rath- 
er than  in  lbs.  per  sq.  inch,  as  the  water 
pressure  is. 

1.  From  your  experiment,  how  many 
inches  of  water  does  the  gas  support  and 
how  many  inches  of  alcohol? 

2.  Which  liquid  is  higher  and  why? 

3.  What  pressure  is  the  gas  balancing, 
other  than  that  of  the  liquids? 

4.  Compute  from  the  reading  of  each 
liquid,  the  pressure  of  the  gas  in  lbs.  per  sq. 
inch. 

B.  Mercury  is  used  in  this  part  of  the  ex- 
periment because  water  would  be  too  light 
for  the  length  of  the  manometers  we  use. 

1.  If  the  atmospheric  pressure  supports  a 
column  of  mercury  30  inches  high,  how  high 
a column  of  water  will  it  support? 

2.  Why  are  water  barometers  not  com- 
monly used? 

Take  the  open  manometer  containing  mer- 
cury and  attach  to  the  short  arm,  a rubber 
tube.  Before  exerting  pressure,  get  a glass 
mouthpiece  which  has  been  sterilized.  This 
should  be  sterilized  before  being  used  again 
by  another  person.  (Put  in  boiling  water  to 
sterilize,  or  wrap  a piece  of  paper  around  the 
mouthpiece.)  When  the  mouthpiece  has 
been  attached,  blow  steadily,  reading  the 
position  of  the  mercury  in  the  two  tubes. 

(Do  not  read  the  points  to  which  it  jumps 
but  the  points  at  which  you  can  hold  it  for 
an  appreciable  length  of  time.)  As  the  mer- 


cury  ascends  in  the  long  tube,  it  descends  in 
the  short  tube,  so  to  get  the  height  of  the 
mercury  which  you  really  held  up,  subtract 
the  two  readings.  Tabulate  all  measure- 
ments and  compute  the  pressure  in  lbs.  per 
sq.  inch. 

3.  How  high  a column  of  water  could  you 
have  supported? 

4.  What  was  the  pressure  of  your  lungs  in 
lbs.  per  sq.  inch? 

5.  How  much  is  this  above  normal  atmos- 
pheric pressure? 


PROBLEM  No.  15 


To  Determine  the  Relation  Between  the  Buuoyant  Force  Exerted  Upon  a Metal  Cylinder 
Immersed  in  Water  and  the  Weight  of  the  Displaced  Water. 

Directions:  Weigh  the  cylinder  accurate- 
ly in  air.  Suspend  the  cylinder  by  means  of 
a thread  and  weigh  it  accurately  when  en- 
tirely immersed  in  water.  The  difference  of 
these  two  weights  is  the  buoyant  force. 

Next,  find  the  weight  of  the  water  displaced 
by  method  A,  B or  C. 

Method  (A):  Measure  the  dimensions  of 
the  cylinder  carefully  in  centimeters  and 
compute  its  volume.  This  will  numerically 
equal  the  weight  in  grams  of  the  water  dis- 
placed. (1)  Why?  Tabulate  measurements. 

Method  (B):  Fill  an  overflow  can  until 
the  water  just  begins  to  run  out  at  the  spout. 

When  the  last  drop  has  run  out,  lower  the 
cylinder  in  the  can  by  means  of  the  thread 
and  catch  in  the  bucket  the  water  that  has 
been  forced  out.  Accurately  obtain  the 
weight  of  this  water.  This  should  also 
equal  the  buoyant  force. 

Method  (C):  Find  the  displacement  of 
the  cylinder  as  follows : Support  a burette  in 
a vertical  position  fitted  with  a rubber  tube 
and  a pinchcock  at  the  lower  end.  Put 
enough  water  in  the  burette  to  come  up  to 
where  the  marks  are,  and  take  the  reading. 

Tie  cylinder  to  a thread  and  lower  into  the 
burette.  Take  reading  again.  The  differ-^ 
ence  between  these  two  readings  gives  the 
volume  displacement  of  the  cylinder,  or,  nu- 
merically the  weight  of  the  displaced  water. 

(1)  Why?  If  time  permits,  take  three  sets 
of  readings  at  different  heights  of  the  tube 
and  find  the  average  of  your  results. 

Record  the  results  in  the  following  form : 

Weight  of  cylinder  in  air 

Weight  of  cylinder  in  water 

Buoyant  force  on  cylinder 

Weight  of  water  displaced 

Difference  

Per  cent  of  difference 

(2)  State  Archimedes’  principle  in  your 
own  words. 

(3)  A cake  of  ice  floating  in  water  is  6 
ft.  square  and  2 ft.  thick.  A man  stepping 
on  it  causes  it  to  sink  one  inch.  Find  the 
weight  of  the  man. 


‘ 

’ 

. 

‘ 

■ 

' 


PROBLEM  No.  16 


To  Find  the  Specific  Gravity  of  an  Irregular  Solid.  Which  Sinks  in  Water. 

Suspend  the  solid  from  the  specific  gravity 
balance  and  weigh  it  in  air.  Then  accurately 
weigh  it  entirely  immersed  in  water. 

1.  What  is  the  difference  in  the  two  weigh- 
ings in  grams? 

2.  According  to  Archimedes’  principle,  to 
what  is  the  loss  of  weight  in  water  equal? 

3.  How  is  the  volume  in  C.C.  obtained? 

4.  What  is  meant  by  the  specific  gravity 
of  a substance? 

Record  your  results  for  several  materials 
as  follows: 

Kind  of  solid 

Weight  in  air 

Weight  in  water 

Loss  of  weight  in  water 

Weight  of  an  equal  volume  of  water 

Specific  gravity  computed 

Specific  gravity  accepted 

5.  A block  of  marble  weighs  5000  g.  in  air 
(sp.  gr.  2.5)  ; how  much  will  it  weigh  in 
water  ? 

6.  Calculate  the  density  of  marble  in  (5). 

(a)  In  metric  units 

(b)  In  English  units 


\ 

v ' • 

. 

- 

< i‘  n ■ iil uoL:'>  r> 

) 


PROBLEM  No.  17 


To  Determine  the  Specific  Gravity  of  a Solid  Lighter  Than  Water. 

Attach  a cord  to  the  body  and  weigh  it. 

Then,  with  a sinker  attached,  weigh  them 
when  the  sinker  is  immersed  in  water  and 
the  body  is  in  the  air.  Next,  weigh  when 
both  body  and  sinker  are  immersed.  Be 
careful  that  the  objects  do  not  touch  the 
sides  of  the  vessel  containing  the  water, 
otherwise  the  true  weights  will  not  be  ob- 
tained. The  difference  between  the  second 
and  third  weighings  is  the  buoyant  effect  of 
the  water  on  the  body  alone. 

1.  Show  clearly  why  this  last  statement  is 
true. 

From  this  data,  calculate  the  specific  grav- 
ity of  the  body,  making  a complete  tabula- 
tion of  your  measurements. 

2.  What  is  the  density  of  this  body? 

3.  What  is  the  distinction,  if  any,  between 
density  and  specific  gravity? 

4.  Are  they  ever  numerically  equal  to  one 
another?  If  so,  when? 


' 


. 

I 


* 


PROBLEM  No.  18 


To  Find  the  Specific  Gravity  of  a Liquid  by  the  “Loss  of  Weight”  Method. 

Directions:  (a)  Weigh  an  irregular  solid 
in  air;  then  in  the  liquid.  The  difference  in 
weight  is  the  weight  of  the  liquid  displaced 
by  the  solid.  (1)  Why?  Next,  weigh  the 
solid  immersed  in  water.  The  difference  be- 
tween this  weight  in  water  and  the  weight  in 
air  equals  the  weight  of  the  water  displaced. 

(2)  Why?  From  these  two  weights,  deter- 
mine the  specific  gravity  of  the  liquid. 

(3)  How? 

(b)  Now  apply  the  hydrometer  to  the 
liquid  and  read  the  specific  gravity,  which 
this  gives.  Compare  this  result  with  your 
other  determination. 

(4)  Which  method,  (a)  or  (b)  is  quicker? 

(5)  Which  result  would  you  judge  to  be 
the  more  accurate  of  the  two  and  why? 

Tabulate  your  results  in  a convenient 
form. 


. 

■ 

' 


V 


PROBLEM  No.  19 


To  Find  the  Specific  Gravity  of  a Liquid  by  Hare’s  Method. 

Arrange  the  apparatus 
according  to  the  diagram. 

Raise  the  liquids  in  the 
tubes  to  a height  of  30 
or  40  cm.  by  a partial 
exhaustion  of  the  air 
through  the  rubber  tube 
at  the  top.  Now  close 
the  tube  air-tight  by 
means  of  the  clamp. 

Watch  the  liquids  in 
the  tubes  for  a few  mo- 
ments to  see  whether  the 
liquids  fall  or  not.  If 
they  do,  it  shows  that  the 
tube  is  not  air-tight. 

Measure  the  vertical 
height  of  the  two  columns  above  the  sur- 
. faces  of  the  liquids  in  the  tumblers.  Make 
three  sets  of  readings,  changing  the  height 
each  time. 

(1)  Why  is  water  used  as  one  of  the 
liquids  ? 

Divide  the  height  of  the  water  column  by 
the  height  of  the  liquid  to  be  measured.  This 
will  give  you  the  specific  gravity  of  the  j 

liquid. 

Devise  a suitable  record  in  tabulated  form 
for  your  readings. 


„V;  ..  , ' ' , • l • — 

>~Vi 

V 

. 

- 


I r^r-lv  : 

. 

iri  . ....  :■  . ..  s 

> . . . 1 -. 

. 

... 


PROBLEM  No.  20 


e 

o 


o 

© 


To  Test  Hooke’s  Law  on  Stretching  by  Means  of  the  Jolly  Balance. 

Adjust  the  spring  and  read  the  position  of 
the  index  before  any  load  has  been  placed  on 
the  pan  and  call  this  the  “zero  reading.” 

Now  place  a weight  of  1 or  0.5  g.,  (let  the 
instructor  determine  this  for  you)  and  adjust 
the  index.  The  difference  between  this  read- 
ing and  the  zero  reading  is  the  stretch  of  the 
spring.  Continue  increasing  the  load  on  the 
pan  by  1 or  0.5  g.  until  ten  trials  have  been 
made  and  record  the  position  of  the  index 
for  each  load.  Compute  the  stretch  for  each 
trial. 

Record  in  a tabulated  form  the  results: 
zero  reading,  position  of  index,  load  and 
stretch. 

1.  What  relation  is  there  between  the  load 
(stress)  and  the  stretch  (strain)  ? 

2.  As  directed,  plot  a graph  to  show  the 
relationship  between  the  strain  and  stress. 

If  the  graph  is  a straight  line,  it  indicates 
that  one  measurement  is  proportional  to  the 
other.  State  Hooke’s  Law  as  shown  by  the 
graph. 

3.  Explain  how  you  can  weigh  accurately 
a small  piece  of  any  substance  with  a Jolly 
balance  and  a single  one  gram  weight. 


' 

! 


PROBLEM  No.  21 


To  Find  the  Breaking  Strength  of  Wires  Composed  of  Different  Materials. 

Measure  with  a micrometer  the  diameter 
of  the  copper  wire  in  three  places.  After 
determining  its  size  with  a standard  wire 
gauge,  consult  a wire  table  and  compare  the 
two  results.  Fasten  the  proper  length  of 
wire  firmly  to  the  tension  balance  and  to  the 
crank  shaft.  Turn  the  crank  handle  slowly 
until  the  wire  breaks.  Repeat  this  process 
three  times  with  each  wire  and  using  the 
average  values  obtained,  calculate  the  break- 
ing strength  in  pounds  for  a wire  made  of 
the  same  material,  one  square  inch  in  cross 
section.  This  number  is  called  its  tensile 
strength  and  is  useful  to  the  engineer  in 
building  bridges,  etc. 

Repeat  the  experiment  using  iron  and 
aluminum  wire. 

1.  How  many  lbs.  will  it  take  to  break  a 
No.  10  copper  wire? 

2.  How  many  lbs.  will  it  take  to  break  a 
No.  10  aluminum  wire? 

3.  What  relation  exists  between  breaking 
strength  and  area  of  cross  section? 


. 

• • ' 

■ ■■ 

. 

. 

, 

■ 

...  ..  . 


PROBLEM  No.  22 


To  Test  the  Freezing  and  Boiling  Points  of  Water  on  a Centigrade  Thermometer. 

To  test  the  freezing  point,  pack  the  bulb  of  , 
the  thermometer  furnished  in  clean  snow  or 
fme  ice,  with  the  zero  mark  far  enough 
above  the  snow  for  you  to  see  it  plainly. 

When  the  mercury  has  sunk  to 
within  one  degree,  begin  to  take 
readings  once  a minute  and  con- 
tinue until  three  successive  read- 
ings are  the  same  to  a tenth  of  a 
degree.  Record  the  last  reading 
as  the  freezing  point,  using  a 
small  hand  lens,  if  convenient,  to 
read  to  tenths  of  a degree.  The 
temperature  of  melting  ice  is 
practically  constant  and  is  de- 
noted by  zero  on  the  Centigrade 
scale.  Find  the  error  in  your 
thermometer  in  degrees  and 
tenths  of  degrees. 

To  test  the  Boiling  Point: 

For  purposes  of  testing  the 
boiling  point,  the  thermometer  is  exposed  to 
the  steam  from  boiling  water.  Suspend  the 
thermometer  within  the  inner  tube  of  the 
hypsometer,  passing  the  stem  through  a 
cork  at  the  top.  If  the  cork  fits  the  stem 
loosely,  slip  a rubber  band  over  the  ther- 
mometer just  above  the  cork.  The  100  de- 
gree mark  should  project  only  one  or  two  de- 
grees above  the  cork  at  the  top,  so  that  as 
much  of  the  stem  as  possible  is  exposed  to 
the  steam.  Fill  the  boiler  of  the  hypsometer 
about  a quarter  full  of  water  and  heat  it  to 
boiling  over  a suitable  burner.  After  the 
steam  has  escaped  freely  for  several  minutes, 
read  the  thermometer  to  tenths  of  degrees 
as  before. 

The  boiling  point  should  not  be  100  degrees 
because  the  pressure  in  the  room  is  not  76 
cm.,  so  that  you  are  not  yet  in  a position  to 
judge  the  correctness  of  your  thermometer 
on  this  point.  It  has  been  found  that  the 
boiling  point  is  lowered  .375  degrees  by  a fall 
of  one  centimeter  in  the  barometric  reading. 

Read  the  barometer  and  compute  the  correct 
boiling  point  by  subtracting  from  100  de- 
grees .375  degrees  centigrade  for  each  cm. 
the  barometer  is  less  than  76  cm.  [or  by 


formula,  true  boiling  point  equals  100 — .0375 
(760  Bar.  reading)]. 

Find  the  error  in  the  boiling  point  recorded 
on  your  thermometer,  considering  your  work 
to  be  accurate. 

Record  your  results  as  follows : 

Height  of  barometer 

Number  of  thermometer 

Thermometer  reading  in  melting  ice 

Error  of  freezing  point 

Thermometer  reading  in  steam 

Correct  temperature  of  steam 

Error  of  boiling  point 

1.  Draw  a graph  according  to  sample. 


1 /PU  r />w 


2.  Would  your  thermometer  give  a correct 
reading  of  the  room  temperature?  Give 
reasons  for  your  answer. 


PROBLEM  No.  23 


To  Determine  the  Effect  of  Pressure  on  the  Boiling  Point  of  a Liquid. 

METHOD  A 

Set  up  the  apparatus  ac- 
cording- to  the  diagram.  Ob- 
serve the  temperature  of  the 
boiling  point  when  the  mer- 
cury levels  in  the  manometer 
are  equal.  Then  allow  the 
steam  to  pass  through  the 
tube  and  very  gradually  close 
the  pinchcock  until  the  mer- 
cury in  the  open  arm  of  the 
manometer  is  3 or  4 cm.  high- 
er than  in  the  closed  arm. 

This  shows  the  pressure  in 
the  boiler  to  be  that  many  cm.  above  atmos- 
pheric pressure.  Record  the  exact  number 
of  cm.  and  the  reading  of  the  thermometer. 

The  difference  between  the  thermometer 
reading  now  and  the  reading  when  the  pres- 
sure was  room  pressure  is  that  caused  by  the 
increase  of  pressure  indicated  by  the  man- 
ometer. Find  the  difference  caused  by  one 
cm.  and  the  per  cent  of  error  from  .375  de- 
grees, the  accepted  value.  Tabulate  your 
results. 

METHOD  B. 

Set  up  the  apparatus  according  to  the  dia- 
gram. Fill  the  flask  one  half  full  of  water. 


zl 

Insert  the  thermometers  and  glass  tube 
through  the  holes  in  the  stopper.  Place  the 
stopper  on  the  neck  of  the  flask.  Heat  the 
water  until  it  boils  freely.  Notice  the  tem- 
perature of  the  steam  and  then  of  the  water. 
Next  remove  the  burner,  place  the  free  end 
of  the  glass  tube  in  the  jar  of  water,  and 
press  down  slightly  on  the  stopper.  Notice 
the  temperature  of  the  water  in  the  flask. 


L 


Hi 


rrf 


y u 


Observe  as  closely  as  possible  at  how  low  a 
temperature  the  water  continues  to  boil. 
Tabulate  your  results. 

1.  Why  is  the  temperature  of  the  steam 
different  from  that  of  the  boiling  water? 

2.  While  the  water  is  heating,  a slight 
amount  of  air  is  leaving  from  the  free  end  of 
the  glass  tube.  Why? 

3.  After  the  burner  is  removed  and  the 
free  end  of  the  glass  tube  placed  in  the  jar 
of  water,  why  does  the  water  go  up  the  tube 
into  the  flask? 

4.  Why  does  the  water  boil  when  cold 

water  enters  the  flask? 

5.  State  the  effect  of  pressure  on  the  boil- 
ing point. 


PROBLEM  No.  24 


To  Find  the  Coefficient  of  Linear  Expansion  of  Some  Metals. 

The  coefficient  of  linear  expansion  is  the 
amount  that  one  centimeter  of  a rod  expands 
when  heated  one  degree  Centigrade,  or  (it  is 
the  fraction  of  its  length  that  a rod  expands 
when  heated  one  degree  Centrigrade) . 

To  find  experimentally  the  coefficient  of 
linear  expansion,  say  of  steel,  we  have  to  take 
a rod  or  tube  of  considerable  length,  heat  it 
through  a certain  number  of  degrees  and 
then  measure  how  much  it  expands.  To  il- 
lustrate, suppose  that  an  iron  tube  whose 
length  is  60  cm.  at  a room  temperature  of 
20  degrees  C.  is  heated  to  100  degrees  C.  and 
as  a result  expands  .0576  cm.  To  find  how 
much  1 cm.  expanded  for  one  degree,  we 
must  take  1/60  times  1/80  of  .0576  cm. 

Working  this  out,  it  is  found  to  be  .000012, 
which  is  the  coefficient  of  linear  expansion  of 
iron. 

In  the  example  given  above,  it  was  stated 
that  a rod  60  cm.  long  expanded  .0576  cm. 
when  heated  80  degrees.  This  expansion  is 
so  small  that  it  cannot  be  measured  directly 
with  sufficient  accuracy.  It  is,  therefore, 
necessary  to  use  some  method  that  will  give 
the  required  degree  of  precision.  There  are 
several  methods  that  are  in  common  use  for 
this  purpose.  The  one  that  we  shall  employ 
is  applied  in  what  is  known  as  a Cowen  linear 
expansion  apparatus.  The  construction  and 
working  of  the  apparatus  must  be  learned 
from  a study  of  the  model  that  is  set  up  for 
that  purpose  in  the  laboratory.  When  you 
understand  the  apparatus,  proceed  to  per- 
form the  experiment.  Take  the  measure- 
ments and  observations  indicated  in  the  ac- 
companying table  and  make  the  required  cal- 
culations for  the  metal  rods  furnished  by  the 
instructor. 

Name  of  metal 

1 2 3 Av. 

Temperature 

of  room  

Temperature 

of  steam  

Rise  of 

temperature  


Number  of  degrees  pointer  turned 

Diameter  of  dial  axis.  .'.  . . .mm cm. 

Circumference  of  dial  axis cm. 

Part  of  complete  revolution  made  by  dial 

axis  

Total  expansion  (indicate  your  work) 

Length  of  tube  between  supports 

Statement: cm.  length  of 

tube  has  expanded cm.  for  a change 

in  temperature  of degrees  C. 

Expansion  for  one  cm.  (equation) 

Expansion  for  one  cm.  for  one  degree  (equa- 
tion)   

The  coefficient  of  linear  expansion  of 

(metal)  is 

Problem:  A surveyor’s  steel  tape  is  100 
feet  long.  Assuming  the  lowest  temperature 
in  winter  to  be  40  degrees  below  zero  C.  and 
the  warmest  in  summer  40  degrees  above 
zero  C.,  what  is  the  maximum  error  per  foot? 
Express  the  amoun  tof  this  error  in  per  cent. 
(Consider  it  correct  at  0 degrees  C.) 


PROBLEM  No.  25 


To  Study  the  Law  of  Heat  Exchange  by  the  Method  of  Mixtures. 

A.  The  law  of  heat  exchange  states  that 
when  two  substances  at  different  tempera- 
tures are  mixed,  the  number  of  heat  units 
lost  by  one  is  equal  to  the  number  of  heat 
units  gained  by  the  other.  The  heat  unit 
used  in  the  metric  system  is  the  calorie  and 
is  defined  as  the  amount  of  heat  required  to 
raise  one  gram  1 degree  C.  In  the  English 
system,  it  is  known  as  the  British  Thermal 
Unit  (B.T.U.)  and  is  the  amount  of  heat  nec- 
essaary  to  raise  one  lb.  of  water  1 degree  F. 

Weigh  a dry  calorimeter  and  place  about 
200  cc.  of  water  into  it.  After  accurately 
weighing  the  two,  heat  the  water  to  50  de- 
grees C.  Into  another  dish  measure  about 
200  cc.  of  water  whose  temperature  is  about 
10  degrees  C.  Now  carefully  take  the  tem- 
peratures of  the  water  in  each  receptacle 
with  separate  thermometers  and  quickly 
pour  the  cold  into  the  hot  water.  Stir  the 
mixture  with  both  thermomters  with  their 
bulbs  held  together  and  take  its  temperature 
near  the  top  of  the  water  and  near  the  bot- 
tom. If  the  readings  differ,  stir  again  and 
then  take  the  highest  uniform  temperature. 

When  you  take  the  thermometers  out  of  the 
calorimeter,  touch  the  bulbs  to  its  side,  that 
the  adhering  water  may  be  removed.  Again 
weigh  the  calorimeter  with  its  contents. 

From  this  data,  calculate  the  following  and 
record  your  results  in  tabular  form : 

A B 

1.  Weight  of  dry 

calorimeter  

2.  Weight  of  calorimeter 

and  warm  water  

3.  Weight  of  warm 

water  

4.  Weight  of  calorimeter 

warm  and  cold  water 

5.  Weight  of  cold  water 

6.  Temperature  of  warm 

water  

7.  Temperature  of  cold 

water  

8.  Temperature  of  the 

mixture  

9.  Calories  of  heat  lost 

by  warm  water  


10.  Calories  of  heat  lost 

by  the  calorimeter  

11.  Total  number  of  cal- 
ories lost  

12.  Calories  (calculated) 

gained  by  cold  water  . . . : 

13.  Difference  between 

the  last  two  items  

If  your  results  are  not  reasonably  close, 
repeat  the  experiment. 

1.  Define  a calorie. 

2.  Is  the  resulting  temperature  an  aver- 
age of  the  two?  If  it  is  not,  how  do  you  ex- 
plain the  difference? 

B.  Repeat  the  experiment,  using  about 
100  cc.  of  warm  water  and  about  250  cc.  of 
cold  water. 

3.  Since  your  results  show  that  some  heat 
has  been  lost,  could  the  calorimeter,  the 
thermometers  or  the  air,  account  for  the  heat 
wasted?  Explain. 


PROBLEM  No.  26 


To  Determine  the  Specific  Heat  of  a Solid. 

To  raise  the  temperature  of  1 gram  of 
water  1 degree  C.,  requires  a unit  quantity 
of  heat  called  the  calorie.  It  is  shown  by 
experiment  that  this  quantity  of  heat  will 
raise  the  temperature  of  1 gram  of  almost 
any  substance  more  than  1 degree  C.  The 
specific  heat  of  any  substance  is  the  number 
of  calories  necessary  to  raise  the  tempera- 
ture of  1 gram  of  that  substance  through  1 
degree  C. 

Suspend  a metal  coil  in  boiling  water  until 
it  has  acquired  the  temperature  of  the  water; 
determine  the  temperature  of  the  water  by 
means  of  a thermometer.  Weigh  a calori- 
meter, fill  it  about  two-thirds  full  of  cold 
water  and  weigh  again.  Determine  the  mass 
of  the  water  and  also  find  its  temperature. 

The  temperature  of  the  water  should  be  low- 
er than  that  of  the  room.  Remove  the 
metal  quickly  from  the  boiling  water  and 
suspend  it  in  the  cold  water  so  that  it  will 
not  touch  the  sides  or  the  bottom  of  the 
calorimeter.  Stir  the  water  with  the  ther- 
mometer until  its  temperature  ceases  to  rise, 
and  record  the  temperature  of  the  water. 

The  mass  of  the  cold  water  times  its  rise, 
would  be  the  number  of  calories  imparted  to 
it  and  hence  lost  by  the  metal.  From  the  re- 
sults determine  the  specific  heat  of  the  metal, 
which  is  the  number  of  calories  required  to 
raise  the  temperature  of  one  gram  of  the 
metal  one  degree. 

Tabulations : 

Kind  of  metal 

Weight  of  calorimeter 

Water  equivalent  (mass  times  sp.  lit.) 

Weight  of  water 

Temperature  of  water  at  beginning 

Mass  of  metal 

Temperature  of  heated  metal 

Final  temperature  of  mixture 

Amount  of  heat  exchanged  (Indicate 

your  work)  

Portion  of  the  heat  exchanged  by  one 
gram  of  the  metal  changing  one 

degree  C 

Specific  heat  of  the  metal  used 

Question : Did  you  actually  find  the 
amount  of  heat  required  to  raise  1 gram  1 de- 
gree C.  or  the  amount  given  off  by  1 gram  in 
cooling  1 degree  C.  ? 


' 


. 


■ 


' 

■ 


PROBLEM  No.  27 


To  Find  the  Dew  Point  of  the  Air  in  the  Laboratory  and  to  Determine  Its  Relative  Hu- 
midity. 

The  dew  point  is  defined  as  the  tempera- 
ture to  which  the  air  must  be  cooled  so  that 
condensation  of  water  vapor  may  occur.  This 
temperature  depends  upon  the  relative 
amount  of  water  vapor  in  the  air  at  that 
time. 

Method:  (a)  To  find  the  dew  point,  put 
some  water  in  a calorimeter  to  about  an  inch 
in  depth.  Have  on  hand  a tumbler  of  water 
and  some  finely  crushed  ice,  or  snow.  Be 
careful  not  to  breathe  on  the  bright  surface 
of  the  calorimeter,  as  the  warm,  moist  breath 
will  produce  an  error  in  your  results.  Add 
ice  to  the  calorimeter,  a very  little  at  a time, 
stirring  constantly  with  the  thermometer. 

Watch  closely  for  the  first  thin  film  of  moist- 
ure neay  the  bottom  of  the  can  and  when  it 
does  appear  take  the  temperature  of  the 
water.  Wipe  the  dew  off  with  a cloth  or 
your  finger  and  observe  whether  the  deposit 
quickly  gathers  again.  If  it  does,  add  a 
small  amount  of  warm  water  and  find  the 
highest  temperature  at  which  the  dew  will 
form.  Take  their  average  as  the  dew  point 
of  the  air  in  the  laboratory  at  the  time  of  the 
experiment.  Make  three  trials  and  record 
each  result  obtained. 

To  determine  the  relative  humidity,  use  is 
made  of  the  ratio  of  the  pressure  exerted  by 
the  water  vapor  in  the  air  at  that  time  to  the 
pressure  of  the  vapor  were  the  air  saturated 
with  it.  To  find  the  various  pressures  ex- 
erted, turn  to  a Table  of  Constants  of  Satu- 
rated Water  Vapor,  as  will  be  found,  for  ex- 
ample, on  Page  171,  Millikan  and  Gale.  Sup- 
pose the  dew  point  were  found  to  be  14  de- 
grees C.  when  the  room  temperature  was  26 
degrees  C.  This  indicates  that  the  amount 
of  moisture  in  the  air  at  26  degrees  C.  would 
saturate  it  at  14  degrees  C.  From  the  col- 
umn P in  the  table,  we  find  that  at  14  degrees 
C.,  the  vapor  exerts  a pressure  of  11.9  milli- 
meters, and  that  had  the  air  been  saturated 
at  26  degrees  C.,  the  vapor  pressure  would 
have  been  25  mm.  Under  these  supposed 
conditions,  the  air  would  have  contained  11.9 
divided  by  25  or  .476,  the  amount  of  moisture 
that  it  would  hold.  So  we  say,  the  relative 
humidity  is  47.6%.  In  a like  manner,  calcu- 
A late  your  result. 


Method:  (b)  Another  means  of  obtaining 

these  results  is  by  using  the  hygrodeik,  which 
employs  wet  and  dry  bulb  thermometers, 
thus  applying  the  principle  of  cooling  by 
vaporization.  If  this  principle  is  not  clear  to 
you,  review  it  in  your  text. 

Fan  the  wet  bulb  until  the  reading  be- 
comes stationary.  Observe  the  readings  of 
the  wet  and  dry  bulbs.  Set  the  sliding  point-  | 
er  at  the  line  on  the  wet  bulb  side  of  the 
chart,  corresponding  with  the  degree  reading 
of  the  wet  bulb  tube;  swing  the  arm  to  the 
right,  to  the  point  of  intersection  with  the 
red  line  curving  from  the  dry  bulb  side  and 
corresponding  to  the  degree  reading  of  the 
dry  bulb  tube.  At  this  intersection,  the  in- 
dex hand  will  point  to  the  relative  humidity 
on  the  scale  at  the  bottom  of  the  chart. 

To  find  the  dew  point,  observe  the  intersec- 
tion as  above,  and  follow  the  heavy  black 
line  passing  through  it,  which  runs  from  the 
top  downward  to  the  right  to  the  point  of 
contact  with  the  dry  bulb  scale.  Compare 
these  results  with  those  obtained  in  method 
(a). 

1.  Of  what  practical  use  is  the  determina- 
tion of  the  dew  point? 

2.  How  would  you  determine  the  relative 
humidity  out-of-doors  on  a very  cold  day  ? 


PROBLEM  No.  28 


To  Discover  the  Latent  Heat  of  Fusion. 

In  general,  when  heat  is  applied  to  a solid, 
its  temperature  rises  until  it  reaches  a point 
where  it  begins  to  pass  into  the  liquid  form. 

Any  further  supply  of  heat  fails  to  produce 
any  rise  in  temperature  while  the  melting  is 
in  progress;  the  heat  used  goes  to  melt  the 
solid.  The  heat  absorbed  by  the  solid  is 
enrgy  converted  into  the  potential  form  in 
the  work  of  giving  mobility  to  the  molecules 
and  is  said  to  become  latent  or  hidden.  As 
soon  as  the  solid  is  melted,  a continued  ap- 
plication of  heat  causes  the  temperature  to 
rise.  Converselv,  when  the  temperature 
falls,  a stationary  point  is  reached  where  the 
solidification  sets  in  and  the  heat  rendered 
latent  on  melting  is  set  free  again.  Under 
the  same  conditions  of  pressure,  the  two  sta- 
tionary temperatures,  that  of  melting  and 
that  of  solidification  coincide.  The  quantity 
of  heat  required  to  convert  one  gram  of  a 
substance  from  the  solid  to  liquid  is  called 
latent  heat  of  fusion. 

To  determine  the  latent  heat  of  fusion  of 
ice  or  snow: 

Dry  and  weigh  the  calorimeter.  Heat  a 
quantity  of  water  to  about  35  degrees  in  the 
beaker.  While  the  water  is  heating,  prepare 
pieces  of  clean  ice  and  place  them  upon  a 
piece  of  cloth  to  absorb  the  water  formed  in 
melting.  Pour  the  water  into  the  calori- 
meter to  within  about  three  cm.  of  the  top 
and  weigh  to  find  the  mass  of  water  taken. 

Stir  the  water  with  the  thermometer  and 
when  the  temperature  is  about  30  degrees, 
begin  to  add  dry  pieces  of  ice. 

Take  the  temperature  of  the  water  at  the 
very  instant  before  the  first  piece  of  ice  is 
dropped  in.  Add  ice  until  the  temperature 
when  all  the  ice  is  melted  falls  to  about  10 
degrees.  Take  the  reading  of  the  ther- 
mometer, the  very  instant  that  the  ice  be- 
comes all  melted  and  weigh  the  calorimeter 
and  contents  to  find  the  mass  of  ice  added. 

By  means  of  the  data  obtained,  answer  the 
following  questions : 

1.  How  much  heat  has  the  warm  water 
given  out  in  cooling? 

2.  What  is  the  rise  in  temperature  of  the 
melted  ice? 


3.  How  much  heat  has  the  calorimeter  giv- 
en out  in  cooling? 

Part  of  the  heat  has  caused  the  ice  to  melt 
and  part  has  raised  the  temperature  of  the 
melted  ice. 

4.  How  much  of  the  heat  given  out  by  the 
calorimeter  and  by  the  water  has  gone  to 
raise  the  temperature  of  the  melted  ice? 

5.  How  much  heat  has  been  used  in  caus- 
ing the  ice  to  melt  without  change  in  tem- 
perature ? 

6.  How  much  ice  was  used? 

7.  How  much  heat  was  needed  to  melt  one 
gram  of  ice  without  changing  the  tempera- 
ture ? 

8.  What  is  the  latent  heat  of  fusion  of  ice  ? 

The  results  may  be  tabulated  as  follows: 

Mass  of  calorimeter,  Water  equivalent  of 
calorimeter,  Mass  of  water  taken,  Mass  of  ice 
added,  Initial  temperature  of  the  water  and 
calorimeter,  Final  temperature  after  mixing, 
Latent  heat  of  fusion  of  ice,  Percentage  of 
error. 


PROBLEM  No.  29 

To  Determine  the  Heat  of  Vaporization  of  Water. 


The  amount  of  heat  required  to  vaporize 
one  gram  of  a substance  without  changing 
its  temperature  is  called  the  heat  of  vapor- 
ization of  that  substance. 

Generate  the  steam  the  same  way  you  have 
before  and  place  a trap  between  the  steam 
supply  and  the  calorimeter  to  guard  against 
the  introduction  of  hot  water  instead  of 
steam.  (1)  How  should  the  trap  be  used  to 
prevent  condensed  steam  from  entering  the 
water?  Weigh  the  calorimeter  and  put  into 
it  about  450  grams  of  cold  water  at  about  10 
degrees  C.  Take  the  temperature  of  the 
water.  Place  a screen  around  the  calorimet- 
er to  prevent  the  loss  of  heat.  When  the 
steam  is  given  off  freely  from  the  boiler,  in- 
troduce sufficient  steam  to  raise  the  temper- 
ature of  the  water  to  about  30  degrees  centi- 
grade, at  the  same  time  constantly  stirring 
the  water  with  the  thermometer.  Before 
turning  off  the  burner,  remove  the  calori- 
meter,  stir  and  take  the  final  temperature. 
Again  weigh  to  find  the  amount  of  steam 
condensed  in  the  water. 

A.  The  number  of  calories  of  heat  taken 
up  by  the  cold  water  is  evidently  the  weight 
of  the  water  times  its  rise  in  temperature. 
(To  the  amount  of  water  must  be  added  the 
water  equivalent  of  the  calorimeter.)  Part 
of  this  heat  was  given  up  by  the  steam  in  con- 
densing and  part  by  the  condensed  steam  in 
being  lowered  to  the  final  temperature. 

B.  The  number  of  calories  of  heat  given 
up  by  the  steam  after  it  has  condensed  is 
equal  to  the  weight  of  the  steam  multiplied 
by  its  fall  in  temperature. 

Subtracting  B from  A,  we  have  the  amount 
of  heat  given  up  by  the  steam  in  condensing. 
This  divided  by  the  weight  of  the  steam 
gives  the  amount  of  heat  given  up  by  one 
gram  of  steam  in  condensing. 

Tabulations: 

1.  Temperature  of  cold  water 

2.  Temperature  of  steam 

3.  Temperature  of  mixture 

4.  Weight  of  cold  water 

(A)  Amount  of  heat  taken  up  by  the  water 

and  calorimeter  

5.  Weight  of  steam 

(B)  Amount  of  heat  given  up  to  the  water 

by  condensed  steam 


6.  Amount  of  heat  give  up  by  the  steam  in 

being  condensed  (A-B) 

7.  Amount  of  heat  give  up  by  one  gram  of 

steam  in  being  condensed 

The  result  just  obtained  is,  of  course,  the 
same  as  the  amount  of  heat  required  to 
change  one  gram  of  boiling  water  into  steam 
without  changing  its  temperature.  This  is 
known  as  the  Heat  of  Vaporzation  of  water. 

2.  Explain  how  a steam  heating  plant 
operates. 

3.  Why  are  burns  from  steam  more  pain- 
ful and  injurious  than  those  from  boiling 
water? 

4.  In  hot,  dry  countries,  water  is  cooled  by 
placing  it  in  porous  earthenware  jars  or  can- 
vas bags.  Explain. 


PROBLEM  No.  30 


To  Find  the  Image  of  a point  in  a Plane  Mirror  and  to  Determine  the  Relation  Between 
the  Angle  of  Incidence  and  the  Angle  of  Reflection. 

In  these  experiments,  use  only  a sharp 
pointed  pencil  and  draw  all  lines  very  fine. 

Designate  the  path  of  all  rays  of  light  by  us- 
ing arrow  heads.  Make  all  construction  lines 
dotted  and  all  lines  representing  rays  con- 
tinuous. 

Draw  a line  across  the  middle  of  a sheet  of 
paper  and  stand  the  mirror  with  its  reflect- 
ing surface  exactly  on  it.  Stick  a pin  (mark 
it  O,  Object)  vertically  about  ten  centimeters 
in  front  of  the  middle  of  this  mirror.  At 
least  lb  cm.  on  either  side  of  the  pin.  place 
the  edge  of  a rule  in  line  with  the  image  of 
the  pin,  sighting  along  the  rule  with  one  eye. 

Without  moving  the  rule,  draw  a fine  line 
along  its  edge  in  each  of  these  positions. 

(Should  you  have  difficulty  in  accurately  lo- 
cating these  sight  lines  by  this  method,  place 
the  eye  in  the  same  plane  as  the  table  top 
where  a good  image  of  the  object  may  be 
seen.  Then  place  a pin  near  the  mirror  and 
another  one  about  8 or  10  centimeters  dis- 
tance, so  that  the  image  of  the  pin,  0.  and 
these  two  sight  pins  appear  to  be  in  the  same 
straight  line.  Align  these  pins  very  care- 
fully, looking  at  their  base,  and  keep  them 
perpendicular  to  the  board.  Remove  the 
sight  pins  and  through  these  holes  draw 
lines.)  After  removing  the  mirror,  continue 
the  two  sight  lines  till  they  meet  back  of  the 
mirror.  This  intersection  locates  the  image 
of  the  point  represented  by  the  pin. 

Mark  this  point  I (Image) . Draw  OR  cut- 
ting the  mirror  line  at  A.  Find  the  differ- 
ence in  length  between  OA  and  IA.  Mark 
the  point  where- the  left  sight  line  cuts  the 
mirror  line,  B,  and  where  the  right  one  cuts 
it,  C.  Call  these  two  lines  BF  and  CH  re- 
spectively. 1.  What  do  these  lines  repre- 
sent? At  C and  B,  erect  perpendiculars  to 
the  mirror  line  on  its  object  side  and  mark 
them  CE  and  BD.  Draw  OB  and  OC. 

2.  What  do  these  lines  represent?  OBD  and 
OCE  are  called  angles  of  incidence  and  DBF 
and  ECU  are  called  angles  of  reflection.  With 
a protractor  measure  the  value  of  each  angle. 

Find  the  difference  between  the  angles  of  in- 
cidence and  reflection  for  each  observation. 


Record  results  in  the  following  form: — 

Length  OA 

Length  IA  

Difference 

Angle  ODD 

Angle  DBF  

Difference  

Angle  OCE 

Angle  ECH 

Difference 

3.  What  does  the  intersection  of  the  two 
lines  back  of  the  mirror  mark?  Why? 

4.  What  angle  does  the  line  01  form  with 
the  mirror? 

5.  Describe  accurately  the  position  of  the 
image. 

6.  Show  by  construction  how  long  a wall 
mirror  must  be  in  order  to  see  the  full  image 
of  your  body. 

7.  Design  the  path  of  the  rays  of  light  in 
a tailor  mirror  of  three  parts  showing  the 
image  of  your  back. 


PROBLEM  No.  31 


To  Verify  the  Formula  Connecting  the  Position  of  an  Object  and  Its  Image  in  a Spher- 
ical Mirror,  and  to  Find  the  Radius  of  the  Mirror. 


The  mirror  formula:  Let  0 be  the  lumin- 
ous point  on  the  principal  axis  of  a concave 
mirror,  OM  a ray  from  0 meeting  the  mirror 
at  M.  Join  OM  and  draw  MI  making  angle 
CMO  equal  to  CMI.  Then  the  intersection  I 
of  MI  and  NO  is  the  conjugate  focus  of  0. 
Since  the  angle  is  bisected  by  MC,  by  geom- 
etry OM:MI:  :OC:CI. 

Let  NF  equal  f,  OM  equal  Do,  MI  equal  Di. 
If  the  aperture  is  small  ON  equals  Do  and  IN 
equals  Di  very  nearly.  OC  equals  Do  minus 
2f,  IC  equals  2f  minus  Di.  Substituting1 
these  values  in  the  above  proportion,  we  have 
Do:Di:Do — 2f:2f — Di.  Equating  the  prod- 
ucts of  the  means  and  extremes 
2Dof — DoDi=DoDi — 2Dif. 

Dif+Dof=DoDi.  Dividing  by  DoDif  we  have 
I/Do+I/Di=I/f. 

Support  the  concave  mirror  on  a holder  at 
the  end  of  the  optical  bench  so  that  its  prin- 
cipal axis  shall  be  parallel  to  the  scale  of  the 
bench.  Attach  the  source  of  light  to  a 
bracket  sliding  on  the  optical  bench.  Ar- 
range so  that  the  light  shall  be  on  a level 
with  the  center  of  the  mirror.  On  another 
bracket,  fix  a small  screen  and  adjust  the 
height  of  the  screen  so  that  it  is  also  on  a 
level  with  the  center  of  the  mirror. 

Place  the  light  100  cm.  from  the  mirror, 
and  adjust  the  screen  so  that  the  image 
formed  on  it  may  be  as  distinctly  focussed  as 
possible.  1.  Note  whether  the  image  is 
erect  or  inverted,  whether  it  is  larger  or 
smaller  than  the  object.  2.  Is  the  image 
real  or  virtual?  Carefully  measure  the  dis- 
tance Do  between  the  object  and  the  mirror 
and  the  distance  Di  between  the  image  and 
the  mirror.  Move  the  light  nearer  to  the 
mirror,  again  adjust  the  screen  and  measure 
Do  and  Di. 


Proceed  thus  to  find  a set  of  corresponding1 
values  of  Do  and  Di,  making  five  trials  in  all. 

3.  Note  as  the  light  is  moved  toward  the  mir- 
ror, the  direction  in  which  the  image  moves. 

4.  Note  also  changes  as  to  size,  etc.,  of  the 
image.  Find  a position  in  which  both  object 
and  image  are  at  the  same  distance  from  the 
mirror.  In  this  case,  Do  equals  Di.  5.  When 
the  object  is  at  the  center  of  curvature  of  the 
mirror,  what  is  the  character  of  the  image 
formed?  Verify  the  result  by  the  parallax 
method  as  follows: 

Set  up  a pin  so  that  its  head  is  about  op- 
posite the  middle  of  the  mirror.  Place  the 
eye  so  as  to  see  both  image  and  object  and  ; 
move  the  head  from  side  to  side,  observing 
that  the  more  remote  object  moves  with  the 
head.  Shift  the  pin  until  the  pin  and  image 
are  at  the  same  point.  Measure  the  distance 
to  the  mirror  and  compare  with  the  value  for 
r (with  that  found  by  first  method). 

6.  What  results  do  you  obtain? 

Tabulate  as  follows: 

Do  Di  f r 


PROBLEM  No.  32 

To  Determine  the  Ratio  of  the  Speed  of  Light  in  Air  to  Its  Speed  in  Llass. 


The  index  of  refraction  of  glass  is  the  ra- 
tio of  the  sine  of  the  angle  of  incidence  in  air 
to  the  sine  of  the  angle  of  refraction  in  glass. 

Draw  a straight  line  on  a piece  of  paper 
and  place  a plate  glass  with  parallel  edges 
flat  on  the  paper  with  one  edge  exactly  along 
this  line.  Place  a pin  at  some  point  A,  Fig. 
(1),  and  another  at  a point  B.  With  a ruler 
sight  through  the  glass  from  B to  the  image 
of  A and  draw  a line  C on  the  paper  along 
the  edge  of  the  ruler.  Be  sure  that  your 
pencil  is  sharp.  A blunt  pencil  will  spoil  the 
experiment. 

Remove  the  glass  plate  and  draw  a line 
BA,  and  a line  MBN  perpendicular  to  the 
plate  line  at  the  point  B.  Draw  a circle  with 
B as  center  and  draw  the  lines  GK  and  FTI 
perpendicular  to  MBN. 

The  image  of  the  pin  A is  seen  in  the  glass 
because  light  starting  from  A passes  through 
the  glass  to  B and  then  through  the  air  to 
the  eye  at  G.  The  image  of  A in  the  glass  is 
in  a new  position.  The  reason  for  this  is 
that  the  light  which  travels  from  A through 
the  glass  to  B is  bent  away  from  the  per- 
pendicular MBN  when  it  enters  the  air  at  B. 
THe  light  when  in  glass  makes  an  angle  r 
with  the  perpendicular  MBN  and  when  in  air 
makes  the  larger  angle  i.  To  prevent  con- 
fusion, the  angle  i in  air  is  always  called  the 
angle  of  incidence  and  the  angle  r in  the  oth- 
er medium  (in  this  case,  glass)  is  always 
called  the  angle  of  refraction.  The  index  of  re- 


fraction  of  glass  is  sine  i ^sine  r.  Sine  i=GK 

GB 

and  sine  r=FH,  but  since  GB=FB  (radii  of 
FB 

the  same  circle)  sine  i GK 

■=■ ^index  of  refrac- 

sine  r FH 

tion. 

Measure  GK  and  FH  carefully  and  calcu- 
late the  index  of  refraction  of  glass  or  the 
ratio  of  the  speed  of  light  in  air  to  its  speed 
in  glass. 

Tabulate  your  results  as  follows: 

Length  of  GK—  cm. 

Length  of  FH=  cm. 

Index  of  refraction  of  g!ass= 

Repeat  the  work  for  three  trials. 

1.  Why  does  an  oar  appear  bent  when 
placed  in  the  water?  Draw  a diagram. 

2.  Why  does  the  sun  appear  larger  in  the 
morning  and  evening  than  at  noon? 

3.  From  your  experimental  results  (aver- 
age) find  the  speed  of  light  in  glass. 


PROBLEM  No.  33 


To  Find  the  Focal  Length  of  a Convex  Lens  by  the  Method  of  Conjugate  Foci. 

Set  up  the  apparatus  according  to  the 
model,  using  a luminous  gas  flame  or  other 
light  source  in  front  of  a cardboard  screen. 

An  L shaped  opening  may  be  cut  in  the  card- 
board to  serve  as  the  object. 

Line  up  the  L,  the  lens  and  the  screen  so 
that  their  centers  shall  all  be  in  a line  paral- 
lel to  the  optical  bench. 

Making  the  distance  from  the  L to  the 
screen,  say  about  100  cms.  for  the  first  trial, 
move  the  lens  back  and  forth  between  the 
cardboards  until  a sharp  image  of  the  L is 
formed  on  the  screen.  Adjust  carefully  and 
try  to  get  the  place  where  the  image  is  most 
distinct. 

Measure  the  distance  from  the  L to  the  op- 
tical center  of  the  lens  and  call  this  Do. 

The  distance  between  the  lens  and  the 
image  is  Di. 

Calculate  the  value  of  focal  length  (f) 
from  the  formula  111 

Do  Di  f 

from  which  f=DoXDi 


Do+Di 

1.  Describe  the  image  as  regards  size,  j 
kind,  position,  etc. 

Without  changing  the  relative  position  of 
the  two  screens,  move  the  lens  away  from  the 
L until  you  secure  another  distinct  image  on 
the  screen.  Measure  object  and  image  dis- 
tance as  before. 

2.  How  does  Do  in  trial  2 compare  with 
Di  in  trial  1 ? Explain. 

Change  the  distance  between  the  two 
screens  by  10  cms.  and  repeat  the  two  cases. 
Make  a third  trial  at  another  distance. 

Tabulate  all  results  in  a neat  form. 

The  case  in  which  the  image  is  larger  than 
the  object  illustrates  the  projection  of  pic- 
tures by  a magic  lantern,  stereopticon  or 
moving  picture  machine. 

The  case  in  which  the  image  is  smaller 
than  the  object  illustrates  the  formation  of 
an  image  in  the  camera. 

3.  What  is  the  advantage  of  an  L shaped 
cut? 

4.  Diagram  the  image  formed  by  T shaped 
cut. 


■ . 


■ 


* 

. 


PROBLEM  No.  34 


To  Find  the  Images  Formed  by  a Converging  Lens,  When  the  Lens  Is  at  Different  Dis 

tanccs  From  the  Object. 

Make  a drawing  showing  lens,  screen  and 
image  in  each  case.  Use  your  optical  bench 
with  a source  of  light  at  one  end  and  direct- 
ly in  front  of  it  a screen  with  an  L-shaped 
window  cut  in  it  to  serve  as  the  object. 

(A)  Now  set  your  lens  at  its  focal  length 
(known  from  previous  Experiment)  from  the 
illuminated  screen.  The  object  is  now  at  the 
principal  focus  of  the  lens.  Move  the  opaque 
screen  on  the  other  side  of  the  lens  and  see 
whether  an  image  is  formed  on  the  screen. 

The  formation  of  an  image  means  that  the 
rays  of  light  leaving  the  lens  converge.  If 
an  image  is  not  formed,  the  rays  leaving  the 
lens  are  either  parallel  or  divergent.  (1) 

When  the  object  is  at  the  principal  focus, 
what  is  the  direction  of  the  rays  of  light 
leaving  the  lens? 

(B)  Move  the  lens  nearer  the  object. 

The  object  is  now  within  the  principle  focus. 

Move  the  screen  to  find  out  whether  an 
image  is  formed.  Look  through  the  lens 
and  describe  its  appearance.  (2)  In  this 
case,  what  do  you  think  is  the  direction  of 
the  rays  leaving  the  lens  ? Explain  by  means 
of  a diagram. 

(C)  Place  the  lens  so  that  the  object  is 
at  twice  the  focal  length.  Place  the  screen 
at  an  equal  distance  on  the  other  side  of  the 
lens.  (3)  Is  the  image  on  the  screen  erect 
or  inverted?  (4)  Is  it  larger  or  smaller 
than  object?  (5)  Compare  the  relative  dis- 
tances from  the  lens  of  object  and  image. 

(6)  At  what  distance  from  a camera  lens 
would  you  place  a drawing  in  order  to  ob- 
tain a photographic  copy  of  the  same  size? 

(D)  Move  the  lens  in  a little  toward  the 
object,  so  that  it  is  at  a distance  greater 
than  the  focal  length  but  less  than  twice  the 
focal  length.  Move  the  screen  till  a sharp 
image  is  formed.  Now  measure!  the  dis- 
tance between  the  lens  and  the  image.  Also 
measure  the  object  distance.  (7)  Compare 
the  image  distance  with  twice  the  focal 
length.  (8)  Note  the  relative  size  of  ob- 
ject and  image. 


(E)  Move  the  lens  to  a point  whose  dis- 
tance from  the  object  is  equal  to  the  image 
distance  obtained  in  (D).  The  object  dis- 
tance is  now  greater  than  twice  the  focal 
length.  Move  the  screen  till  a sharp  image 
is  formed.  (9)  Note  relative  size  of  object  j 
and  image.  Measure  the  object  distance 
and  image  distance  as  in  (D).  (10)  com- 

pare the  image  distance  in  this  case  with  the 
focal  length  and  twice  the  focal  length. 

(11)  State  the  two  cases  of  conjugate  foci 
shown  in  these  experiments. 

Tabulate  your  focal  length  and  distance 
for  each  of  three  trials.  Then  average  re- 
sults. 

(12)  Where  will  the  screen  for  a stereop- 
ticon  be  located  with  reference  to  the  focal 
length  of  the  objective  lens? 

(13)  Where  will  the  lantern  slide  be  lo- 
cated ? 

(14)  What  is  the  least  distance  from  a 
cgn verging  lens  at  which  an  object  can  be 
placed  in  order  that  a real  image  may  be 
formed  ? 

(15)  State  a general  relation  between  the 
size  of  the  object  and  image  and  their  re- 
spective distances  from  the  lens. 


PROBLEM  No.  35 


To  Construct  an  Astronomical  Telescope  and  Find  Its  Magnifying  Power. 


1.  Set  up  a convex  lens  of  fairly  long 
focal  length  across  the  room  from  the  win- 
dow. Adjust  a screen  until  you  get  a clear 
real  image  of  the  wire  netting  on  the  win- 
dow. Set  up  another  convex  lens  of  small- 
er focal  length  in.  a line  with  the  first,  the 
screen  on  which  the  first  image  was  formed 
being  at  the  focal  length  of  the  second  one. 
Remove  the  screen  and  look  thru  both  of 
the  lenses  at  the  wire  netting.  If  the  work 
is  done  correctly,  the  netting  will  be  seen 
clearly,  enlarged  and  inverted.  The  first 
lens,  called  the  objective,  forms  a real  in- 
verted image  at  a distance  approximately  its 
focal  length.  This  image  is  smaller  than 
the  object.  The  second  lens,  called  the  eye 
piece,  takes  this  image  as  an  object  and 
forms  a virtual,  erect  and  enlarged  image. 
Even  though  the  image  formed  by  the  ob- 
jective is  smaller  than  the  object,  the  sec- 
ond lens  magnifies  enough  so  as  to  produce 
on  the  retina  of  the  eye  an  image  larger  than 
that  obtained  by  the  eye  alone,  looking  at 
the  object  without  the  aid  of  the  two  lenses. 
Notice  that  the  image  formed  by  the  objec- 
tive is  inverted,  while  that  formed  by  the 
eye  piece  is  erect,  hence  the  object  as  seen 
through  the  telescope  is  inverted.  As  the 
'astronomical  telescope  is  used  to  view  only 
heavenly  bodies,  it  is  not  important  that  an 
erect  image  be  obtained. 

2.  To  find  the  magnifying  power  of  the 
telescope,  draw  two  lines  on  the  black-board, 
four  or  five  inches  apart  and  set  up  the  tel- 
escope at  as  great  a distance  as  possible  so 
that  they  may  be  clearly  seen  through  the 
telescope.  Then  looking  at  the  lines,  one  eye 
through  the  telescope,  the  other  half  shut  di- 
rectly at  the  board,  have  a fellow  student  in- 
dicate by  dots  on  the  board  the  apparent  posi- 
tion of  the  lines  as  seen  through  the  tele- 
scope. In  this  work,  be  careful  to  have  the 
best  focus  with  the  eye  which  is  looking 
through  the  telescope.  The  magnifying  pow- 
er is  the  apparent  distance  between  the  lines 


as  shown  by  the  distance  between  the  dots 
divided  by  the  real  distance  between  the  lines 
themselves.  Measure  the  distances  and  find 
the  ratio.  The  theoretical  magnifying  power 
of  an  astronomical  telescope  is  the  focal 
length  of  the  objective  divided  by  the  focal 
length  of  the  eye  piece. 

Make  a tabulation  showing  the  focal 
lengths,  distance  between  lenses,  real  dis- 
tance between  lines  and  apparent  distance 
between  lines,  magnifying  power  as  comput- 
ed and  theoretical  magnifying  power. 

a.  Draw  a diagram  of  the  astronomical 
telescope,  showing  the  lenses  and  position  of 
images  formed  by  each. 


PROBLEM  No.  36 


To  Construct  an  Erecting  Telescope  Using  a Convex  and  Concave  Lens. 


A 


Whenever  an  object  is  seen  by  the  eye,  the 
lens  of  the  eye  forms  a real,  inverted,  small 
image  of  the  object  on  the  retina  of  the  eye, 
the  retina  serving  as  a screen.  The  nerve 
endings  of  the  optic  nerve  compose  the  reti- 
na. The  impression  produced  by  the  image 
is  transmitted  by  the  optic  nerve  to  the 
brain.  Even  though  the  image  on  the  retina 
is  inverted,  the  brain  by  some  means  makes 
us  see  the  object  erect.  In  the  case  of  the 
erecting  telescope,  the  convex  lens,  which  is 
used  as  an  objective,  forms  a real  image. 
The  concave  lens,  used  as  an  eye  piece,  is 
placed  so  as  to  diverge  the  rays  which  have 
come  from  the  objective  sufficiently  to  have 
the  image  produced  by  the  objective  formed 
on  the  retina  of  the  eye.  The  image  is  larg- 
er than  it  would  be  without  the  telescope. 
The  effect  of  the  eye  piece  is  to  neutralize 
the  crystalline  lens  of  the  eye.  which  is  a 
convex  lens,  the  magnification  being  due  to 
the  objective. 

Set  up  a convex  and  a concave  lens,  using 
the  convex  as  the  objective  and  the  concave 
as  an  eye  piece  and  view  some  object  at  a 
considerable  distance,  e.g..  the  screens  on 
the  windows  from  across  the  room.  Have 
the  concave  lens  near  the  eye  and  move  the 
convex  lens  away  from  you  until  you  obtain 
a clear  image.  Estimate  the  magnification 
produced.  Draw  a diagram  showing  the  re- 
lative position  of  the  objective,  eve  piece  and 
the  eye.  and  the  position  of  object  and  image. 
Record  the  estimated  magnifying  power. 

1.  Look  at  the  object  through  the  concave 
lens  alone.  What  kind  of  an  image  is  form- 
ed, real  or  virtual,  inverted  or  erect,  large  or 
small  ? 


- 


. 

. 

( 

' 


PROBLEM  No.  37 


To  Find  the  Rate  of  Vibration  of  a Tuning  Fork  by  the  Siren  Disc  Method. 

Use  the  motor  rotator  with  the  siren  disc 
attached  and  a tuning  fork  whose  vibration 
rate  you  wish  to  find.  Rotate  the  disc  and 
by  means  of  a rubber  tube  and  a glass  tube 
drawn  to  a point,  produce  a musical  tone  by 
blowing  a jet  of  air  across  one  of  the  rows 
of  holes  on  the  disc.  (For  regulating  the 
speed  of  the  motor,  there  is  a rheostat  built 
into  the  base  of  the  motor.  By  moving  the 
lever,  the  motor  is  made  to  rotate  faster  or 
slower.)  Sound  the  tuning  fork  by  striking 
with  the  rubber  mallet  given  you  and  place 
the  stem  of  the  fork  on  some  wooden  surface 
so  as  to  make  the  sound  of  the  fork  readily 
heard.  Change  the  speed  of  the  motor  until 
the  tone  given  by  the  jet  blown  across  the 
row  of  holes  is  the  same  as  that  of  the  fork. 

This  will  be  difficult  to  do,  as  the  motor  will 
probably  vary  in  speed.  Make  trials  until 
the  tone  seems  constant  and  then,  by  means 
of  the  speed  indicator  and  a watch,  count  the 
number  of  revolutions  made  by  the  rotator 
in  one  minute.  This  will  require  consider- 
able practice.  One  person  may  keep  time, 
giving  the  signals  to  begin  and  stop  count- 
ing, and  the  other  may  do  the  counting. 

Count  by  tens.  It  is  evident  that  the  speed 
indicator  may  not  be  registering  on  a ten 
when  the  first  signal  is  given,  nor  when  the 
second  signal  is  given,  so  it  will  take  a little 
thought  and  skill  to  get  a correct  count.  Hav- 
ing the  number  of  revolutions  in  one  minute, 
compute  the  number  per  second,  and  find  the 
vibration  rate  of  the  tone  given,  by  multiply- 
ing by  the  number  of  holes  in  the  row.  (The 
tone  is  produced  by  the  stopping  of  the  air 
current,  thus  causing  condensations  and 
rarefactions  to  be  sent  through  the  air.) 

The  result  of  your  readings  and  computations 
is  to  be  compared  with  the  number  on  the 
fork. 

Make  a tabulated  record  containing  the 
number  of  revolutions  per  minute,  the  num- 
ber of  revolutions  per  second,  the  number  of 
holes  in  the  row,  the  computed  number  of 
impulses  per  second  causing  the  tone,  the 
number  of  vibrations  per  second  as  regis- 
tered on  the  fork  and  the  difference. 

1.  Which  row  of  holes  on  the  disc  would 
give  the  highest  tone  and  why? 

2.  Do  you  think  the  number  on  the  fork  is 
exactly  correct?  Give  reasons. 


' 

* 

iJH  <*f! ' 


PROBLEM  No.  38 

To  Find  the  Vibration  Rate  of  Any  Vibrating  Body  by  the  Resonator  Method. 


The  variable  resonator  used  in  this  experi- 
ment may  consist  of  either  a large  glass  tube 
with  a close  fitting  piston,  or  a cylindrical 
jar  or  tube  into  which  water  may  run.  Strike 
the  body  with  a wooden  or  rubber  mallet  to 
set  it  vibrating  and  place  it  at  the  opening  of 
the  I'esonator,  parallel  to  the  reflecting  sur- 
face. While  it  is  sounding,  slowly  draw  the 
& piston  back,  (or  introduce  water)  till  the 
first  position  of  maximum  sound  is  reached. 
Be  sure  that  the  true  position  of  resonance 
has  been  accurately  located  and  mark  it  by 
means  of  a small  rubber  band.  Carefully 
measure  the  length  of  this  air  column,  which 
is  one-fourth  of  a wave  length  of  the  tone 
given  by  the  vibrating  body,  with  a correc- 
tion dependent  on  the  diameter.  It  is  found 
that  the  size  of  the  glass  affects  the  length 
of  this  air  column  in  such  a way  that  if  two- 
fifths  of  its  diameter  be  added,  the  length  of 
the  air  column  for  a given  vibrating  body 
will  be  the  same  for  all  sizes  of  resonators 
used.  Add  this  correction  and  obtain  the 
full  wave  length.  Calculate  the  velocity  of 
sound  at  the  room  temperature  by  adding  to 
the  velocity  at  zero  degrees  C.  (331  3M)  o.G 
m.  for  each  degree  above  that  mark.  With 
these  corrected  values,  calculate  the  number 
of  vibrations  of  the  sounding  body  bv  the 
formula  V=NL,  or  N=V/L. 

Record  your  results  as  follows: 

Temperature  of  room 

Velocity  of  sound  at  this  temperature 

Number  of  vibrating  body 

Diameter  of  resonator  tube 

One-fourth  wave  length.  Trial  1 

Trial  2 Average 

Full  wave  length.  (Corrected) 

Vibration  rate 

If  the  resonator  is  long  enough,  locate  in 
the  same  way  a second  position  of  resonance 
with  a longer  air  column.  Mark  this  place 
with  a second  rubber  band.  The  distance  be- 
tween the  two  positions  of  maximum  reso- 
nance is  one-half  a wave  length  of  the  note 
sent  forth  by  the  vibrating  body.  1.  Why 
isn’t  it  necessary  to  make  a diameter  correc- 
tion this  time?  Measure  this  distance  and 
from  this  data,  obtain  the  full  wave  length. 
Compare  it  with  the  value  obtained  above. 


Again  using  the  formula  N=V/L,  compute 
the  vibration  rate.  Repeat  the  experiment 
with  different  bodies  and  take  two  trials  for 
each  one. 

Compare  the  results  obtained  here  with 
those  obtained  in  the  first  part  of  this  ex- 
periment. 


PROBLEM  No.  39 


To  Find  the  Velocity  of  Sound  in  Air  by  the  Resonance  Method. 

Loudest  resonance  is  secured  when  the  air 
column  is  one- fourth  of  a wave  length  of  the 
tone  given  by  the  fork.  Resonance  is  also 
produced  when  the  air  column  is  three- 
fourths  of  a wave  length  or  any  odd  number 
of  fourths  of  a wave  length  of  the  tone  given 
by  the  fork.  It  is  evident  that  for  each 
longer  distance  the  resonance  will  not  be  so 
good,  for  the  sound  in  traveling  the  longer  . 
distance  has  lost  some  of  its  intensity  and 
will  not,  therefore,  be  so  loud.  If  the  best 
resonance  is  secured  with  the  shortest  reso- 
nating air  column  (one-fourth  of  a wave 
length)  and  resonance  again  with  the  air 
column  three-fourths  of  a wave  length,  the 
difference  is  one-half  of  a wave  length,  and 
the  diameter  of  the  tube  does  not  have  to  be 
considered. 

Run  the  piston  forward  into  the  resonator 
tube  until  it  is  within  three  or  four  inches  of 
the  open  end.  Set  the  tuning  fork  in  vibra- 
tion by  bringing  it  down  against  the  striking 
board  with  moderate  force  and  then  hold  it 
opposite  the  open  end  of  the  tube.  As  the 
fork  vibrates,  draw  the  piston  slowly  back 
into  the  tube  until  the  first  point  of  resonance 
is  found.  Move  the  piston  back  and  forth 
several  times  while  the  fork  is  vibrating, 
till,  judging  by  the  loudness  and  clearness 
of  the  sound,  you  are  certain  the  correct  posi- 
tion for  best  resonance  has  been  found.  Place 
one  of  the  wire  markers  at  this  point  on  the 
tube. 

Since  the  next  position  of  resonance  will 
be  three-quarters  of  a wave  length  from  the 
mouth  of  the  tube,  draw  the  piston  back 
into  the  tube  approximately  three  times  the 
length  of  the  first  resonance  column.  Then, 
sounding  the  fork  as  before,  move  the  piston 
back  and  forth  until  the  second  point  of  best 
resonance  has  been  located  as  accurately  as 
possible.  Set  the  second  marker  at  this 
place.  (The  sound  produced  at  this  second 
position  of  resonance  will  not  be  as  loud  as  at 
the  first  position  because  in  the  second  case 
the  fork  has  to  set  three  times  as  much  air 
in  vibration.)  Measure  the  distance  be- 
tween the  markers  and  record  it  as  “trial  1.” 

Next  displace  the  markers  and  proceed  to 


locate  the  same  points  of  resonance  two 
times  more.  When  this  lias  been  done,  find 
the  average  of  the  three  values  thus  obtain- 
ed.' Repeat  the  experiment  with  as  many 
forks  as  you  have  time  to  use.  Calculate  the 
value  of  1 and  record  the  number  of  vibra- 
tions stamped  on  the  fork.  Letting  V stand 
for  the  velocity  of  sound  at  the  temperature 
of  the  experiment,  we  have 
V=  nl 

Substitute  the  values  of  n and  1 in  this  and 
find  V.  Since  we  cannot  compare  this  with 
the  velocity  at  zero  degrees,  we  must  reduce 
V to  the  velocity  at  zero.  As  the  velocity 
changes  .6  m per  degree  change  in  tempera- 
ture, we  have 

Vo=V — .6t 

in  which  Vo  stands  for  the  velocity  at  zero 
degrees  Centigrade.  Compare  this  result 
with  331.3  m.,  the  standard  value  for  the 
velocity  of  sound  If  your  result  is  more 
than  2r/r  off  from  the  standard,  do  the  ex- 
periment over  again. 

Neatly  tabulate  the  results  for  all  trials. 
Include  in  the  tabulated  record:  (1)  Half 
a wave  length,  (2)  Wave  length,  (3)  Num- 
ber on  fork,  (4)  Velocity  as  computed  from 
experiment  at  room  temperature,  (5)  Tem- 
perature of  room,  (6)  Computed  velocity  at 
0 degrees  and  (7)  Difference. 


PROBLEM  No.  40 


To  Test  the  Law  of  Lengths  of  Vibrating  Strings. 

The  law  says  that  the  vibration  rate  of  a 
string  is  inversely  proportional  to  the  length, 
i.e.,  the  longer  the  string,  the  lower  the  rate 
of  vibration  in  exact  proportion.  A string 
two  times  as  long  vibrates  one-half  as  fast; 
a string  three  times  as  long  vibrates  one- 
third  as  fast ; etc. 

Use  a sonometer  and  by  means  of  the  mov- 
able bridge  obtain  the  length  of  wire  which, 
when  made  to  vibrate,  will  give  the  same 
tone  as  the  lowest  of  the  eight  forks  of  the 
diatonic  scale,  C.  Change  the  length  of  the 
string  after  having  recorded  the  measure- 
ment and  make  two  more  trials  for  the  same 
fork.  Average  the  lengths  obtained.  Re- 
peat for  three  trials  for  the  D fork  and  aver- 
age as  before.  Use  the  proportion,  256  (C) 
is  to  288  (D)  as  the  average  of  the  lengths 
for  D is  to  the  average  of  the  lengths  for  C, 

(inverse  proportion)  and  find  the  product  of 
the  means  and  the  product  of  the  extremes. 

Their  equality  will  determine  the  truth  of 
the  law,  considering  your  work  to  be  abso- 
lutely exact  in  every  respect,  and  the  num- 
ber on  the  forks  to  be  correct.  If  your  prod- 
ucts are  cloqn  enough,  considering  errors,  to 
warrant  your  drawing  the  conclusion  that 
the  law  holds  in  the  experiment,  you  may 
continue. 

It  is  evident  that  if  all  the  forks  of  the 
diatonic  scale  be  used  in  a similar  manner, 
the  product  of  the  means  and  extremes  as 
you  use  them  is  really  the  product  of  the  vi- 
bration rate  in  each  case  and  the  correspond- 
ing length.  (Did  you  not,  in  the  first  pro- 
portion, multiply  288  by  the  length  of  the 
string  you  obtained  for  that  vibration  rate, 
and  256  by  its  corresponding  leng-th?)  If 
you  realize  this,  it  will  not  be  necessary  to 
write  out  the  proportion  in  full  each  time. 

Instead,  you  may  merely  multiply  each  vi- 
bration rate  (number  on  the  fork)  by  the 
length  you  obtain  for  that  fork,  and  compare 
those  products. 

Use  all  the  forks  of  the  scale  E,  F,  G,  A, 

B,  C,  as  indicated  and  record  all  measure- 


ments,  etc.,  in  a neat  tabulated  form,  show- 
ing all  products  of  means  and  extremes. 

1.  What  is  a sonometer?  Draw  a figure. 

2.  Do  you  consider  that  your  products  are 
near  enough  alike  to  prove  the  law  in  the  ex- 
periment as  performed? 

3.  Is  there  any  other  way  of  testing  a pro- 
portion than  equating  the  product  of  means 
and  extremes? 

4.  Why  do  small  errors  show  up  large  in 
equating  the  products  of  the  means  and  ex- 
tremes ? 


PROBLEM  No.  41 


To  Test  the  Law  of  Tensions  of  Vibrating  Strings. 

The  law  says  that  the  vibration  rate  of  a 
vibrating  string  is  directly  proportional  to 
the  square  root  of  the  tension  or  stretching 
weight,  e.g.,  if  the  tension  in  one  case  is  four 
times  as  much  as  it  is  in  another  case,  the 
vibration  rate  is  two  times  as  much,  or  if 
the  tension  is  nine  times  as  much,  the  vibra- 
tion rate  is  three  times  as  much. 

Use  a sonometer,  and  three  sets  of  two 
forks  each,  the  vibration  ratios  of  the  forks 
in  each  set  being  2 to  3,  e.g.,  C and  G,  F and 
c,  and  G and  d.  Put  a tension  of  four  lbs.  or 
four  kg.  on  the  wire,  and  move  the  sliding 
bridge  until  the  vibration  rate  of  the  wire 
when  bowed  or  plucked  is  the  same  as  that 
of  the  lower  fork  in  set  number  one,  as  near- 
ly as  you  can  judge.  Make  the  trial  very 
carefully  to  be  sure  you  have  the  tone  as 
nearly  like  that  of  the  fork  as  you  can  make 
it.  Then  increase  the  tension  to  9 lbs.  or 
kg.  (use  the  same  weight  unit  as  before) 
and  compare  the  tone  produced  by  it  when 
vibrating  with  the  second  fork  of  set  num- 
ber one. 

1.  How  does  the  vibration  rate  of  the  wire 
under  the  second  tension  compare  with  that 
of  the  second  fork? 

2.  What  is  the  ratio  of  the  square  roots  of 
the  two  tensions  used? 

Again  put  a tension  of  4 units  of  weight 
on  the  wire  and  move  the  bridge  until  the 
wire  vibrates  with  the  rate  of  that  of  the 
first  fork  in  set  number  two,  F.  Letting 
the  bridge  remain  stationary,  put  on  the  wire 
a tension  of  9 units,  and  compare  the  vibra- 
tion rate  under  this  tension  with  that  of  the 
second  fork  in  the  set,  c. 

3.  How  does  it  compare? 

Repeat  the  process  with  the  third  set  of 
forks. 

4.  How  does  the  vibration  rate  of  the  sec- 
ond fork  in  set  number  three  compare  with 
that  of  the  wire  under  the  second  tension? 

5.  Do  you  feel  that  the  results  of  the  ex- 

periment justify  you  in  saying  that  the  law 
holds  true  under  the  conditions  you  have 
taKen . f 


6.  Use  the  law  and  solve: — If  a wire  un- 
der 36  oz.  tension  vibrates  384  times  a sec- 
ond, how  fast  will  it  vibrate  if  the  tension  is 
increased  to  64  oz.  ? Show  the  numbers  sub- 
stituted in  the  proportion.  What  note  will 
this  be  if  384  is  G? 


PROBLEM  No.  42 


To  Compare  the  Speed  of  Sound  in  Brass  With  That  in  Air 

Use  the  apparatus  furnished.  See  that 
the  rod  is  clamped  at  its  middle  point.  Dis- 
tribute the  cork  dust  evenly  along  the  tube 
from  one  disc  to  the  other.  Now  produce  a 
clear  musical  tone  by  rubbing  the  rod  with  the 
cloth  on  which  a little  powdered  rosin  has 
been  sprinkled.  A slight,  steady  pressure  will 
be  found  most  effective.  After  rubbing  once 
or  twice,  adjust  the  movable  disc,  moving  it 
a very  short  distance,  say  two  or  three  milli- 
meters. Continue  to  excite  the  rod  and  ad- 
just the  length  of  the  air  column  alternately, 
moving  the  disc  always  in  the  same  direction, 
until  the  dust  begins  to  be  agitated.  After 
this,  only  a slight  further  adjustment  will  be 
needed  to  produce  fairly  sharp  nodes.  The 
final  adjustment  is  most  easily  made  by  ro- 
tating the  tube  a little  on  its  supports,  so  that 
the  dust  lying  in  the  disturbed  regions  be- 
tween the  nodes  will  slide  down,  while  the 
nodes  themselves  will  be  marked  by  fairly 
sharp  peaks  of  dust  projecting  up  the  sides  of 
the  tube.  With  a meter  stick,  determine  the 
length  of  the  brass  rod  .and  from  this  length 
and  a study  of  the  diagram,  determine  the 
half  wave  length  of  sound  in  brass. 

Find  the  distance  between  the  successive 
nodes  in  the  air  column.  Do  not  measure 
single  segments,  but  select  two  nodes  as  far 
apart  as  possible  and  measure  the  distance 
between  these.  Divide  the  distance  by  the 
number  of  intervening  segments  and  thus  ob- 
tain the  average  length  of  one  segment. 

(Repeat  the  readings  until  you  have  a set  of 
average  readings.) 

The  ratio  of  the  wave  lengths  in  brass  and 
air  is  the  ratio  of  their  velocities.  Compute 
the  velocity  in  brass  from  the  velocity  in  air 
at  room  temperature. 

Tabulate  all  readings,  computations  and 
results. 

Questions : 

1.  Could  you  determine  the  speed  of  sound 
in  any  substance  that  could  be  put  in  the 
form  of  a rod? 

2.  Give  all  the  steps  in  the  process  of  rea- 


A\uvyj  = 


soning  used  in  reaching  your  conclusion. 


_vVAyf_  j, 


PROBLEM  No.  43 


To  Map  the  Magnetic  Fields  of  (1)  a Bar  Magnet,  (2)  a Horse-shoe  Magnet,  (3)  Two 
Magnetic  Poles  of  Unlike  Kind,  (4)  Two  Magnetic  Poles  of  Like  Kind,  (5)  Two  Un- 
| like  Poles  With  a “Keeper”  Placed  Mid-way  Between  Them. 


Directions: 

1.  Use  a compass  and  locate  the  poles  of  a 
bar  magnet.  Place  a sheet  of  paper  above 
a bar  magnet  and  sift  iron  filings  over  it, 
tapping  the  paper  gently  to  facilitate  the  ar- 
rangement of  the  filings.  Draw  a figure  to 
show  the  arrangement.  Always  place  ar- 
rows on  drawings  to  show  the  direction  of 
the  lines  of  force. 

2.  Use  a horse-shoe  magnet  similarly. 

3.  Place  the  ends  of]  two  bar  magnets' 
about  an  inch  apart  so  that  opposite  poles 
face  each  other,  and  proceed  as  before. 

4.  Arrange  two  bar  magnets  as  in  3,  but 
with  like  poles  facing  each  other. 

5.  Place  a piece  of  soft  iron  between  the 
unlike  poles  as  in  3,  but  not  touching  either 
pole  and  note  the  arrangement  of  the  filings, 
making  a drawing  as  before. 

Questions : 

1.  Which  cases  indicate  attraction  and 
which  repulsion? 

2.  What  is  a compass?  Explain  its  ac- 
tion. 

3.  What  is  declination? 


. 


' 


■ 


PROBLEM  No.  44 

To  Determine  How  Bodies  May  Be  Magnetized  and  Study  the  Theory  of  Magnetism. 

Directions: 

a.  Stroke  a knitting  needle  or  other  thin 
piece  of  steel  with  a bar  magnet,  being  sure 
to  stroke  from  the  center  of  the  needle  to-  ! 
ward  one  end  with  the  N.  pole  of  the  magnet 
and  toward  the  other  end  with  the  S.  pole. 

Test  the  polarity  of  the  needle  and  state  how 
it  became  a magnet-. 

b.  After  testing  carefully  the  polarity  of 
the  magnetized  knitting  needle,  cut  it  in  two 
nearly  equal  pieces  with  a wire  cutter  and 
test  the  polarity  of  each  half.  Cut  each  half 
into  smaller  pieces,  testing  the  polarity  each 
time.  1.  How  long  might  this  process  be 
continued?  2.  What  may  be  considered  the 
units  of  which  a bar  magnet  is  composed? 

c.  Bring  the  N.  pole  of  a bar  magnet  near 
the  head  of  a small  nail  or  brad  but  not  in 
contact  with  it.  (Place  a small  piece  of  pa- 
per or  glass  between  the  magnet  and  nail  to 
keep  them  apart  if  necessary.)  3.  Does  the 
magnet  attract  the  nail?  Remove  the  mag- 
net. Hold  the  point  of  the  first  nail  near  the 
head  of  a second  nail.  4.  Does  it  attract  the 
second  nail?  Now  bring  the  N.  pole  of  the 
bar  magnet  near  the  head  of  the  first  nail. 

5.  Does  the  first  nail  receive  the  power  to  at- 
tract the  second?  6.  By  what  method  were 
the  nails  magnetized?  Determine  and  mark 
the  polarity  of  the  ends  of  the  two  nails. 

d.  Take  an  ordinary  soft  iron  rod,  about  3 
inches  long,  wind  ordinary  insulated  copper 
wire  about  ten  times  around  it  and  pass  an 
electric  current  through  the  wire.  Test  the 
ends  of  the  rod  for  polarity  while  the  current 
is  passing  through  the  wire.  7.  Is  the  rod 
magnetized?  By  what  means?  Repeat  the 
experiment  with  about  twenty  turns  of  wire. 

8.  What  difference  do  you  observe? 

e.  Hold  a demagnetized  rod  in  a north  and 
south  plane  with  the  north  end  dipping 
downward  at  an  angle  of  about  70  degrees 
with  the  horizontal.  With  the  rod  held  in 
this  position,  strike  it  near  each  end  several 
smart  blows  with  a hammer.  Test  the  pol- 
arity of  the  rod.  Reverse  the  rod,  tap  again 
and  test  for  its  polarity.  Now  hold  the  rod 


in  a horizontal  position  with  its  ends  point- 
ing east  and  west  and  strike  again.  Test 
its  polarity  and  state  clearly  the  results  in 
each  case.  9.  How  was  the  rod  magnetized 
in  this  case?  10.  State  the  theory  of  mag- 
netism. 


PROBLEM  No.  45 


To  Determine  the  Distribution  of  Magnetism  in  a Bar  Magnet. 

The  working  principle  of  this  experiment 
is  to  measure  the  amount  of  force  (express- 
ed in  centimeters  stretch  of  the  spring)  nec- 
essary to  pull  a small  piece  of  soft  iron  away 
from  the  magnet  at  different  points  along  its 
length.  In  order  to  do  this,  suspend  a small 
piece  of  soft  iron  from  the  balance  spring  in 
place  of  the  scale  pans.  Make  such  neces- 
sary adjustments  that  the  scale  is  balanced 
so  the  index  swings  free.  When  in  this  posi- 
tion, take  the  reading  at  the  middle  or  point- 
er as  the  zero  reading,  and  record  it.  Insert 
the  bar  magnet  into  the  holder  so  that  each 
end  is  the  same  distance  from  the  zero  or 
center  scale  of  the  slide.  Next,  place  the 
holder  on  the  shelf.  Adjust  the  holder  so 
that  the  soft  iron  piece  suspended  from  the 
spring  will  drop  into  the  hole  on  the  holder 
when  the  spring  is  lowered.  Finally,  the 
shelf  must  be  pushed  up  to  a height  so  that 
the  soft  iron  just  touches  the  magnet. 

Starting  with  the  N.  pole  of  the  magnet, 
make  the  necessary  adjustments  so  that 
when  the  test  piece  is  lowered,  it  will  make 
contact  with  the  magnet  as  near  the  end  as 
possible.  Then  either  lower  the  shelf  or  raise 
the  spring  as  directed  until  the  test  piece  is 
drawn  away  from  the  magnet.  The  differ- 
ence between  this  reading  and  the  zero  read- 
ing is  the  stretch.  Make  three  trials  and 
average.  In  a like  manner,  take  three  trial 
readings  for  points  one  centimeter  apart  on 
the  magnet.  .If  one  of  the  trial  readings 
should  differ  too  much  from  the  other  two, 
discard  it  and  take  another  reading  to  obtain 
a value  more  nearly  in  ag'reement  with  the 
other  two. 

Plot  a graph  to  show  the  relation  between 
the  distances  on  the  magnet  and  the  stretch 
of  the  spring,  that  is,  to  represent  the  dis- 
tribution of  the  magnetism  in  the  bar.  To 
do  this,  lay  off  on  the  bottom  of  the  cross 
section  paper,  spaces  to  represent  the  total 
lengh  of  the  bar.  On  the  left  hand  side  of 
the  sheet,  lay  off  spaces  to  represent  the  cen- 
timeters of  stretch  of  the  spring.  Begin 
with  0 at  the  bottom  and  number  towards 
the  top,  choosing  a unit  that  will  bring  the 


largest  stretch  near  the  top  of  the  sheet. 
Locate  all  reference  points  and  then  draw  a 
smooth  curve  taking  the  general  direction  of 
the  dots. 

(1)  How  do  you  find  the  magnetism  to  be 
distributed  in  the  bar? 


PROBLEM  No.  46 


To  Study  the  Nature  of  Electric  Charges  by  Means  of  an  Electroscope. 

Rub  a piece  of  ebonite  with  flannel.  Stroke 
it  with  a proof  plane  and  apply  directly  to 
the  knob  of  an  electroscope.  The  electro- 
scope is  now  charged  negatively.  1.  What 
happened  to  the  leaves? 

Discharge  the  electroscope  by  touching  it 
with  the  finger  and  then  recharge  it  positive- 
ly from  the  glass  rod  rubbed  with  silk.  2. 

Why  do  the  leaves  behave  the  same  as  when 
charged  negatively?  While  the  electroscope 
is  still  charged,  touch  the  knob  with  a dis- 
charged ebonite  rod,  a meter  stick,  and  fin- 
ally your  finger.  3.  Which  is  the  better 
conductor  ? 

An  electroscope  may  be  charged  also  by 
induction.  To  do  this,  charge  a glass  rod  by 
rubbing  it  with  silk  and  by  bringing  it  near 
the  knob  of  the  electroscope,  but  not  in  con- 
tact with  it,  till  the  leaves  diverge  about  one 
inch.  There  is  now  an  induced  negative 
charge  on  the  knob  and  an  induced  positive 
charge  on  the  leaves.  While  still  holding  the 
glass  rod  there,  touch  the  knob  with  the  fin- 
ger. 4.  What  happens  to  the  leaves?  5. 

What  charge  must  have  passed  off  through 
the  finger?  Remove  the  finger  first  and 
then  the  rod.  The  negative  charge  that  now 
spreads  to  the  leaves  was  “bound”  by  the  in- 
ducing glass  rod  and  could  not  get  away  even 
when  “grounded”  by  the  finger. 

To  prove  that  the  elecroscope  is  now 
charged  negatively,  rub  an  ebonite  rod  with 
flannel  and  bring  near  the  knob.  The  great- 
er divergence  of  the  leaves  shows  that  the 
leaves  and  the  rod  are  alike,  for  like  charges 
repel.  6.  Why  would  not  the  convergence  of 
leaves  be  a test  for  positive  charges  ? 7.  How 
is  an  insulated  conductor  charged  permanent- 
ly by  induction?  8.  Why  must  the  body  be 
insulated?  9.  What  must  be  the  condition 
of  an  electroscope  before  it  is  useful  in  deter- 
mining the  kind  of  charge  on  a body? 

Charge  the  electroscope  by  induction. 

Take  the  following  substances:  (a)  glass,  1 
(b)  ebonite,  (c)  sealing  wax,  (d)  shellac  and 
(e)  wood.  Rub  each  one  in  succession  with 
fur,  flannel  and  silk.  By  means  of  an  elec- 
troscope, determine  the  sign  of  a charge  on 
each  after  each  rubbing.  Test  for  both  neapa- 


tive  and  positive  charges.  Tabulate  as  fol- 
lows : 

I II  III  IV 


Substances  Charge  on  Behavior  Sign  of 
rubbed  to-  electroscope  of  leaves  charge 
gether 


Glass  with 
fur 

Etc 


PROBLEM  No.  47 


To  Show  That  Static  Electricity  Is  Directly  Connected  With  Current  Electricity  and 

Magnetism. 


~l 


qmsx ► 

& 

Place  a sensitive  compass  needle  on  the 
table  and  allow  it  to  come  to  rest.  Now, 
place  a knitting  needle,  as  shown  in  the  dia- 
gram, exactly  at  right  angles  with  one  end 
of  the  compass  needle.  Connect  the  termin- 
als of  the  coil  on  the  glass  tube  with  a charg- 
ed Leyden  jar.  When  the  spark  passes, 
watch  the  compass  needle- for  attraction  or 
repulsion.  Repeat  the  experiment  with  the 
Leyden  jar  charged  from  the  other  terminal 
of  a static  machine. 

(1)  Does  a current  flow  through  the  wire? 

Using  an  electroscope  and  a proof  plane, 

determine  the  sign  of  the  charge  used  in  each 
trial.  Charge  the  electroscope  positively  by 
induction,  then  touch  the  proof  plane  to  the 
terminal  of  the  static  machine.  Now,  move 
the  proof  plane  near  the  charged  electroscope 
and  decide  the  sign  of  the  charge  from  the 
behavior  of  the  leaves  on  the  electroscope. 

(2)  Have  you  established  a connection  as 
stated  in  the  problem  ? 


■ 


PROBLEM  No.  48 


To  Study  the  Magnetic  Effects  of  an  Electric  Current. 

I.  Use  about  two  meters  of  ordinary  bell 
wire  and  a magnetic  needle.  Connect  up  the 
wire  in  circuit  with  a source  of  current  and 
contact  key  or  circuit  breaker.  Determine 
the  direction  of  the  current  in  circuit  under 
the  directions  of  the  instructor. 

Let  the  magnetic  needle  come  to  rest  point- 
ing north.  Place  the  wire  above  the  needle 
with  the  current  flowing  north.  Complete 
the  circuit  and  note  the  deflection  of  the  N. 
pole  of  the  needle,  whether  east  or  west. 

(The  direction  of  the  deflection  of  the  N.  pole 
indicates  the  assumed  direction  of  the  lines 
of  force.) 

Repeat  the  experiment  with  the  current 
flowing  North  below  the  needle. 

(1)  With  a north  flowing  current,  what  is 
the  direction  of  the  magnetic  field  below  the 
wire  and  above  the  wire?  (East  or  west  in 
each  case.) 

(2)  The  magnetic  field  is  continuous 
around  the  wire.  If  you  were  facing  the 
north  and  looking  down  on  the  wire  under 
the  above  conditions,  what  is  the  direction  of 
the  lines  of  force  at  the  right  and  left  of  the 
wire  respectively,  up  or  down. 

The  thumb  rule  says  that  if  a wire  is 
grasped  with  the  right  hand  with  the  thumb 
pointing  in  the  direction  of  the  current,  the 
fingers  will  encircle  the  wire  in  the  direction 
of  the  lines  of  force. 

Grasp  the  wire  according  to  the  thumb 
rule,  thumb  pointing  north. 

(3)  Indicate  the  direction  of  the  lines  of 
force  below  and  above  the  wire  respectively. 

(4)  Do  these  directions  correspond  to  the 
answers  to  question  1 ? 

Repeat  the  experiment  with  the  current 
flowing  south  above  and  below  the  needle. 

(5)  Indicate  the  direction  of  the  lines  of 
force  below  and  above  the  wire,  whether  east 
or  west. 

(6)  What  are  the  directions  of  the  lines  of 
force  in  this  case  compared  with  those  when 
the  current  was  flowing  north? 

Fry  the  thumb  rule  with  the  thumb  point- 
ing south.  (7)  Does  the  indicated  direction 


of  the  lines  of  force  correspond  to  the  experi- 
mental results? 

Make  a loop  with  one  turn,  the  current 
flowing-  north  above  and  south  below  the 
magnetic  needle  and  note  the  amount  of  de- 
flection compared  with  one  wire  alone.  Make 
a similar  loop  with  two  turns  and  again  with 
several  turns  and  observe  the  action  of  the 
needle. 

(8)  What  is  the  general  .effect  of  increas- 
ing the  number  of  turns? 

(9)  Do  you  think  a small  current  in  a loop 
of  a hundred  turns  would  affect  a sensitive 
magnetic  needle? 

(10)  What  is  the  difference  between  mov- 
able magnet  and  movable  coil  galvanometers  ? 

II  (1)  State  the  converse  of  the  thumb  I 
rule,  showing  how  to  find  the  direction  of  the 
current  in  a wire  when  the  direction  of  the 
magnetic  field  around  the  wire  is  known. 

Test  and  determine  the  direction  of  a cur-  | 
rent  indicated  by  the  instructor  by  using  a 
magnetic  needle  and  above  rule  and  have  it 
verified. 

(2)  Were  your  conclusions  correct  at  the 
first  trial? 

III.  Wind  a coil  of  50  or  60  turns  of  wire 
around  an  iron  rod.  Remove  the  rod  and, 
passing  a current  through  the  coil,  present 
its  ends  in  turn  to  the  N.  pole  of  the  magnetic 
needle.  (Press  the  turns  closely  together  so 
as  to  make  the  force  noticeable.) 

(1)  What  effects  do  you  observe? 

Thrust  the  iron  rod  into  the  coil  and  re- 
peat the  experiment. 

(2)  What  effect  has  the  iron  core? 

Determine  the  direction  of  the  current 

around  the  coil  and  apply  what  is  known  as 
the  thumb  rule  for  coils  to  discover  the  N. 
pole.  Test  your  results  by  presenting  this 
pole  to  the  N.  pole  of  the  magnetic  needle. 

(3)  What  happened? 

(4)  Write  out  the  thumb  rule  for  coils. 

(5)  Name  five  electrical  devices  having 
electro  magnets  as  essential  parts. 


PROBLEM  No.  49 


To  Learn  How  to  Connect  Up  Various  Bell  Circuits. 

In  connecting  up  the  following  bell  circuits, 
practice  economy  in  the  use  of  wires;  that  is, 
use  the  least  number  that  will  accomplish  the 
purpose.  Make  a neat  diagram  to  show  how 
the  connections  are  made  in  each  case.  In 
doing  this,  represent  the  wires  by  straight 
lines  and  have  them  turn  square  corners. 

Use  a small  square  to  represent  the  bell  and 
a small  circle  for  the  key  or  push  button. 

1.  Place  two  buzzers,  (or  bells)  on  one  side 
of  the  table  and  one  key  on  the  other.  Con- 
nect these  into  a circuit  with  electric  current 
so  that  upon  closing  the  key  both  buzzers  will 
sound.  Be  sure  that  the  circuit  is  so  con- 
nected that  should  one  buzzer  be  out  of  order 
and  so  not  sound,  the  other  would  give  a sig- 
nal. While  only  two  buzzers  are  used  in  this 
experiment,  the  connection  must  be  such  that 
more  might  be  sounded  from  the  same  key. 

An  illustration  of  this  kind  of  a circuit  is  the 
bell  system  in  the  school  where  the  master 
clock  in  the  office  closes  one  key  and  rings  all 
the  bells. 

2.  Place  one  buzzer  on  one  side  of  the  table  | 
and  two  keys  on  the  other  side.  Connect  : 
these  into  a circuit  so  that  the  buzzer  may  be 
sounded  from  either  key.  A good  example  of 
this  kind  of  connection  is  to  be  found  in  the 
street  cars,  where  the  bell  for  signaling  the 
motorman  may  be  rung  from  a great  many 
buttons. 

3.  Place  one  buzzer  and  one  key  at  one  side 
of  the  table  and  another  buzzer  and  key  at 
the  other  side.  Connect  these  in  a circuit  so 
that  both  buzzers  will  sound  from  either  key. 

Such  a system  is  used  where  two  different 
rooms  or  places  are  to  be  signaled  at  the  same 
time  from  two  or  more  points. 

4.  Place  the  buzzers  and  keys  the  same  as 
in  (3),  connect  them  in  such  a circuit  that 
pressing  the  key  at  either  side  of  the  table 
will  ring  the  bell  at  the  other  side.  An  ex- 
ample of  this  kind  of  circuit  is  in  the  home 
where  the  push  button,  at  the  front  door 
operates  the  bell  and  the  one  at  the  rear  door 
operates  the  buzzer. 

5.  Diagram  the  wiring  for  the  following  ; 


arrangement,  using  the  least  number  of  wires 
possible.  A 4-family  flat,  of  which  each 
apartment  is  equipped  with  a bell  for  the 
front  door  signal  and  a buzzer  for  the  rear. 
The  current  is  supplied  either  by  a common 
battery,  or  by  a bell  ringing  transformer, 
which  is  located  in  the  basement. 

6.  Make  a large  diagram  showing  the 
course  of  the  current  through  an  electric 
bell.  Use  arrows  to  trace  the  current.  Ex- 
plain its  action. 


PROBLEM  No.  50 


To  Determine  the  Effect  Produced  on  the  E.  M.  F.  of  a Battery  by  Connecting  the  Cells 
in  Series  and  in  Parallel. 

The  voltmeter  readings  must  be  taken  as 
accurately  as  possible.  First  see  if  the 
needle  is  at  zero.  If  not,  make  an  allowance 
for  this  with  every  reading  taken. 

Connect  the  voltmeter  to  each  of  the  cells 
separately  to  see  if  all  are  good.  Dry  cells 
in  good  condition  should  register  about  1.5 
volts.  Edison  primary  batteries  have  an  E. 

M.  F.  of  from  .66  to  .7  volts.  If  any  cell 
shows  a voltage  less  than  it  should,  see  that 
it  is  replaced  by  a good  one  before  going 
ahead  with  the  experiment.  Next,  join  any 
two  of  the  dry  cells  in  series  and  obtain  their 
combined  voltage.  Then  join  three  dry  cells 
in  series  and  obtain  their  combined  voltage. 

Next,  connect  two  of  them  in  parallel  and  fin- 
ally three  in  parallel  and  take  the  voltmeter 
indication  for  both.  Proceed  in  the  same 
manner  to  find  the  E.  M.  F.s  of  the  same 
combination  of  Edison  primary  cells.  Record 
all  these  observations  in  the  tabular  form 
shown  below. 

1.  What  effect  do  you  find  that  series  con- 
nection has  on  the  E.  M.  F.  of  a battery? 

2.  What  effect  is  produced  by  parallel  con- 
nection ? 


1 

1 Cell  connections  | E.  M.  F. 

j 1 

1 

1 1 

! 1 

! Av.  of  all 

1 L 

1 Two  in  S 

1 Three  in  S 

! Two  in  P 

1 Three  in  P 

i 

. 


PROBLEM  No.  51 


To  Show  the  Relation  That  Exists  in  a Circuit  Between  the  Resistance  and  the  Fall  of  Po- 
tential or  Pressure. 


Set  up  the  apparatus  as  shown  in  the  dia- 
gram, using  a meter  of  high  resistance  wire, 
e.  g.,  German  silver,  or  nichrome,  stretched 
along  a meter  stick.  V is  a voltmeter.  The  im- 
portant thing  in  connecting  up  this  circuit  is 
to  have  the  wires  from  the  plus  terminals  of 
the  battery  and  the  plus  binding  post  of  the 
voltmeter  joined  to  the  same  end  of  the  re- 
sistance wire. 

Having  connected  the  apparatus  as  shown 
in  the  figure,  set  the  sliding  key  at  a point  20 
centimeters  from  the  end  A.  Press  the  key 
and  take  the  voltmeter  reading  as  accurately 
as  possible,  allowing  for  any  error  at  the  zero 
and  estimating  all  readings  to  tenths  of  the 
smallest  scale  division.  Proceed  in  this  way 
to  obtain  the  P.D.  across  the  other  lengths 
called  for  in  the  tabular  form.  Obtain  the 
resistances  of  each  of  the  lengths.  (Resist- 
ance of  1 mil  ft.  of  German  silver  is  114  ohms 
and  of  nichrome  wire  660  ohms.) 


(1)  What  relation  do  you  find  to  exist  be- 
tween the  resistances  of  parts  of  a circuit 
and  the  P.D.s  across  the  respective  parts  ? 


Length 
of  wire 

Resistance 

P.  D. 

| 

|(P.  D.  : R) 

L1=20 

R = 

E,= 

L„=40 

R2= 

E,= 

L3=60 

R,= 

e3= 

1 

L4=70 

r4= 

K= 

1 

L,=90 

R,= 

E,= 

1 

i 


■ ■ ; 

. 

' 


. 

PROBLEM  No.  52 

To  Study  the  Laws  of  Induced  Currents. 

Since  the  galvanometer  is  to  be  used  to  de- 
termine the  direction,  as  well  as  the  existence 
of  induced  currents,  it  is  first  necessary  to 
observe  the  direction  of  the  deflection  of  al 
current  whose  direction  is  known.  1.  Dia- 
gram the  arrangement  of  the  apparatus 
showing  the  deflection  of  the  galvanometer 
needle  bv  a known  current. 

Use  a single  cell,  or  a current  designated  by 
the  instructor,  for  this  purpose,  but  before 
closing  the  circuit,  connect  the  terminals  of 
the  galvanometer  with  a short  wire,  which 
will  act  as  a shunt  to  the  galvanometer,  per- 
mitting only  a small  fraction  of  the  current 
to  pass  through  it.  (This  is  a necessary  pre- 
caution with  a sensitive  instrument.)  Ob- 
serve the  direction  of  the  current  from  the 
battery  connections,  also  the  direction  of  the 
deflection.  A current  entering  by  the  other 
terminal  would  cause  a deflection  in  the  oppo- 
site direction.  Hence,  in  the  experiments, 
the  direction  of  the  deflection  will  indicate  by 
which  terminal  the  current  enters  the  gal- 
vanometer; and  from  this,  the  direction  of 
the  current  can  be  traced  through  the  entire 
circuit. 


Connect  the  galvanometer  with  the  large 
coil  of  wire  called  the  secondary  coil.  The 
connections  must  be  a meter  or  more  long. 
2.  Why?  The  circuit  consists  of  the  coil,  the 
galvanometer  and  the  connecting  wires. 

Thrust  the  north  pole  of  a magnet  sudden- 
ly up  to  the  coil  while  observing  the  galvan- 
ometer. Note  the  direction  of  the  deflection. 
Observe  the  effect  of  removing  the  magnet. 
Repeat  until  you  are  sure  of  the  results. 
From  the  direction  of  the  deflection  deter- 
mine whether  the  induced  current  makes  the 
end  of  the  coil  near  the  magnet  a north  pole 
or  a south  pole.  Apply  the  right  hand  rule. 

3.  Draw  diagrams  showing  the  polarity  of 


the  magnet  and  the  direction  in  which  it 
moves,  and  the  resulting  polarity  of  the  coil 
and  the  direction  around  it. 

4.  Is  there  a current  when  the  magnet  is 
at  rest?  5.  What  is  the  experimental  evi- 
dence? Study  the  effect  when  the  south 
pole  is  used  instead  of  the  north  pole. 

Repeat  your  experiments  with  an  electro- 
magnet in  place  of  the  bar  magnet  and  com- 
pare results.  6.  Draw  diagrams  to  indicate 
results. 

7.  What  effect  does  the  rate  of  change  in 
the  magnetic  lines  of  force  have  upon  the 
strength  of  the  induced  currents?  Review 
the  subject  of  magnetic  induction  in  your 
laboratory  experiments  with  the  laws  of 
magnetic  induction. 


PROBLEM  No.  53 


— ^ 


To  Test  Fuses. 

Every  electric  circuit  should  be  provided 
with  some  form  of  protective  apparatus,  so 
that  when  a “short”  is  formed  on  the  line,  the 
great  current  which  would  flow,  would  neith- 
er burn-out  or  damage  the  instruments.  One 
other  great  danger  is  that  a shorted  line  may 
cause  a fire  through  a heated  wire.  It  is  for 
this  reason  that  the  insurance  companies  re- 
quire that  all  lighting  and  power  circuits  be 
protected  by  a fuse.  There  is  one  other 
protective  device,  called  a circuit  breaker. 
Instead  of  fusing,  this  automatically  cuts  off 
the  source  of  energy.  These  circuit  break- 
ers are  used  on  heavy  lines  where  a large 
current  is  carried  and  where  there  is  a ten- 
dency for  overloading  the  line.  They  occupy 
more  space  than  do  fuses,  are  more  costly, 
but  on  the  other  hand,  are  more  convenient. 

Fuses  are  made  of  strips  of  fusible  metal, 
generally  lead  alloyed  with  a small  amount  of 
tin.  Sometimes  zinc  is  used  and  at  times 
copper  or  aluminum  forms  the  fusible  metal. 
Such  metal  is  chosen  as  will  fuse  or  “blow” 
before  any  excess  current  can  flow  through 
the  line.  Copper  is  not  used  to  such  a great 
extent  because  it  heats  and  does  not  fuse  at 
a low  temperature.  In  all  the  fuses  the  heat 
must  be  generated  faster  than  it  can  be  radi- 
ated, or  the  metal  would  not  melt.  After  it 
has  fused,  there  is  a tendency  of  the  metallic 
vapor  to  cause  an  arc.  This  would  make  a 
fuse  too  slow  acting.  To  remedy  this,  the 
cartridge  (or  enclosed)  type  has  a non-in- 
flammable substance  packed  about  the  metal, 
which  immediately  condenses  and  absorbs  the 
vapor  formed.  One  other  form  (expulsion 
type)  provides  a means  for  expelling  the  hot 
vapor.  A third  type  (the  open  fuse)  is  not 
very  dependable  because  of  the  air  currents 
and  the  chemical  action  of  the  elements  on 
them.  Then  if  the  fuse  is  open  and  large, 
the  discharge  of  the  molten  metal  is  dan- 
gerous. 

Wherever  a valuable  apparatus  is  used,  it 
is  a wise  policy  to  use  a fuse  in  the  circuit, 
for  the  fuse  will  cost  ten  cents  or  less,  where- 
as the  instrument  will  probably  cost  twice 
that  many  dollars. 

PROBLEM:  To  test  various  fuse  wires;  to 


show  how  circuits  are  protected  by  fuses. 

Directions:  A.  Connect  the  fuse  block 
with  a suitable  resistance  and  have  a 20  amp- 
Ammeter  in  series  with  it. 

Put  a one  amp.  fuse  wire  in  the  block  and 
slowly  cut  out  resistance  until  the  fuse  is 
blown.  Record  the  reading  of  the  ammeter 
just  as  it  is  blown. 

Repeat  this,  using  such  other  fuse  wire  as 
the  instructor  directs. 

1.  Under  your  discussion,  tell  briefly  what 
was  done,  sketch  the  connections  and  put 
down  your  results  in  tabular  form.  Then 
answer  the  following: 

2.  The  one  amp.  fuse  was  found  to  carry 
% overload  before  blowing. 

3.  Do  the  same  for  the  other  wires  tested 
if  you  know  their  listed  capacity. 

4.  How  many  different  kinds  of  fuse  plugs 
do  you  know  of?  Name  them. 

5.  Did  the  fuse  explode? 

6.  Why  should  it  be  enclosed? 

7.  How  does  a fuse  protect  a circuit? 

B.  Measure  the  diameter  of  the  fuse  wires 
and  see  if  there  is  any  ratio  between  the 
cross  section  area  and  the  amount  of  current 
rent  that  fuses  it. 

C.  In  place  of  regular  fuse  wire,  insert 
copper  wires  and  get  their  maximum  carry- 
ing capacity. 

1.  Notice  if  their  action  of  fusing  differs 
from  the  first  wires  used  and  if  so,  in  what 
respect.  2.  Compare  the  cross  sections  with 
the  load  they  carry.  3.  Do  you  think  the 
length  of  the  wire  used  would  vary  its  carry- 
ing capacity?  4.  If  so,  how? 


PROBLEM  No.  54 


To  Find  Resistance  of  1 Lamp  and  Compare  With  “n”  Lamps  in  Series. 


Directions:  Arrange  five  lamps  in  series 
or  so  that  the  current  has  but  one  path  thru 
all  the  lamps. 

Connect  the  instruments  as  shown  in  dia- 
gram of  connections,  making  sure  that  the 
ammeter  is  in  series  with  the  lamps  while 
the  voltmeter  has  one  free  wire  or  traveler. 
Before  closing  the  switch,  have  the  circuit 
examined  by  your  instructor. 

Read  the  ammeter  and  take  a set  of  read- 
ings with  voltmeter,  getting  first  the  differ- 
ence of  potential  for  1 lamp,  then  2,  3,  4 and 
5 together  by  moving  the  traveler  along  the 
row  of  lamps  and  connecting  at  1,  2,  3,  4 and 
5 respectively.  Disconnect  the  voltmeter  and 
find  the  P.D.  across  each  lamp  singly. 

Arrange  the  circuit  with  only  four  lamps 
in  series. 

Take  another  set  of  ammeter  and  voltmet- 
er readings.  Continue  this  method  of  cut- 
ting out  one  lamp  at  a time  until  only  one 
lamp  is  left. 

Record  all  readings  in  tabular  form.  Cal- 
culate the  ohms  by  means  of  Ohm’s  law 
P.D. 

(Rr= ) for  each  lamp,  two,  three,  four, 

I 

etc.,  lamps  in  series  respectively. 

Find  average  resistance  of  all  single  lamps. 

1.  Do  the  volts  increase  or  decrease  as  you 
increase  number  of  lamps  between  the  volt- 
meter wires  ? 

2.  How  does  the  resistance  of  2,  3,  4,  etc., 
lamps  compare  with  that  of  one?  (Average.) 

3.  Explain  the  brightening  up  of  the  lamps 
as  first  one  and  then  another  is  cut  out. 

4.  What  is  meant  by  “fall  of  potential?” 

5.  What  method  was  used  in  determining 
resistances  in  above  problem? 


. 


>,  • *v 


PROBLEM  No.  55 


To  Find  the  Resistance  of  “n”  Lamps  in  Parallel  and  Compare  With  That  of  One  Alone. 


Connect  the  lamps  with  ammeter  and  volt- 
meter as  shown  in  diagram.  Observe  care- 
fully directions  previously  given  for  connect- 
ing the  instruments  into  the  circuit.  Have 
the  circuit  examined  by  the  instructor  before 
closing  the  switch. 

Lamps  may  be  cut  out  of  circuit  by  simply 
unscrewing  from  the  sockets. 

Take  a set  of  readings  on  each  lamp  by  it- 
self, recording  amperes  and  volts.  Then 
commence  at  the  same  end,  leaving  lamps  on, 
and  take  readings  for  2,  3,  4,  etc.,  together. 


Tabulate  as  follows: 

Let  r=average  resistance  of  single  lamp 
readings. 

n=number  of  lamps. 


I 

1 

E 

E 

R= — 

I 

r | 
R— — 
n 

1 

1 

1.  How  c 

oes  the  resistance  of  2,  3,  4,  etc., 

lamps  in  parallel  compare  with  that  of  one 
alone?  (Average.) 

2.  Why  is  there  no  dimming  of  the  lamps 
as  in  the  series  experiment? 


' 


■* 


PROBLEM  No.  56 


A.  To  Measure  Resistances  by  Means  of  a Slide  Wire  Bridge. 


Directions:  Set  up  the  apparatus  accord- 
ing- to  the  diagram,  using  a D’Arsonval  or 
other  sensitive  galvanometer.  Use  the  cur- 
rent furnished. 

The  difficulty  is  to  get  the  movable  contact 
key  in  such  a position  that  there  will  be  no 
deflection  of  the  galvanometer  needle,  when 
contact  is  made.  First  of  all,  test  the  gal- 
vanometer to  see  that  it  is  in  good  working 
condition.  Handle  it  carefully  for  it  is  a 
delicate  instrument.  Every  galvanometer 
has  some  arrangement  whereby  the  coil  is 
held  stationary  when  not  in  use.  If  you 
move  the  galvanometer  when  the  coil  is 
swinging  freely,  you  will  probably  break  the 
supporting  ribbon.  Always  see  that  the  coil 
is  made  secure  before  leaving  it  or  when 
moving  the  instrument. 

After  seeing  that  you  have  a galvanometer 
in  good  working  condition,  move  the  contact  ! 
key  to  one  end  of  the  bridge  and,  making 
contact,  notice  the  direction  of  the  deflection 
of  the  galvanometer.  Move  the  contact  key 
to  the  other  end  of  the  bridge  and  make  con- 
tact. The  direction  of  the  deflection  of  the 
needle  should  be  opposite.  If  not,  either  of 
the  sets  of  connections  at  the  ends  of  the 
bridge  are  broken.  Trace  connections  and 
make  trials  until  the  deflection  when  contact 
is  made  at  one  end  of  the  bridge  is  opposite 
to  that  at  the  other  end. 

By  trials,  find  a point  where  with  contact 
of  key,  no  deflection  of  the  galvanometer 
needle  is  obtained.  Then  the  ratio  of  the  un- 
known resistance  to  the  known  resistance 
will  be  equal  to  the  ratio  of  the  lengths  of 
the  high  resistance  wire  on  the  correspond- 
ing sides.  R:X::D:D2.  Use  the  proportion 
and  compute  the  value  of  the  unknown  re- 
sistance. 


(Wheatstone.) 


Find  in  this  way  three  unknown  resist-  j 
ances  furnished  by  the  instructor,  making- 
three  trials  for  each,  with  two,  five  and  ten 
ohm  coils  respectively.  Make  a neat  tabula- 
tion showing  known  resistance  used,  length 
of  high  resistance  wire,  proportions  and  val- 
ues  for  the  unknown  resistance,  indicating  j 
what  the  unknown  resistance  is. 

B.  To  Measure  the  Resistance  of  the  Three 
Resistances  Just  Found,  (1)  In  Series,  (2) 
In  Parallel. 

Connect  the  three  resistances  you  have 
just  found  in  series  and  find  by  the  same  ' 
method  their  resistance  for  three  trials,  us-  5 
ing  as  before  two,  five  and  ten  ohm  known 
coils.  Compare  the  average  result  of  these 
trials  with  the  sum  of  the  separate  resistance 
as  found  above.  Tabulate  completely  your 
results. 

Connect  the  three  resistances  in  parallel 
and  similarly,  for  three  trials,  find  the  resist- 
ance. Compare  the  average  with  the  resist- 
ance as  found  bv  the  formula 

111 

R r,  r, 

where  R is  the  total  resistance  in  parallel,  r, 
the  resistance  of  one  coil  alone,  and  r2  the 
resistance  of  the  other  alone.  Tabulate  com- 
pletely the  results. 


PROBLEM  No.  57 


To  Measure  the  Amount  of  Electrical  Energy  Expended  in  Any  Part  of  a Circuit  and  to 
Learn  to  Calculate  the  Energy  in  Watts  When  Any  of  the  Following  Pair  of  Values 

Is  Given: 


1.  Current  and  P.D. 

2.  Resistance  and  P.D. 

3.  Current  and  Resistance. 

The  number  of  watts  of  energy  expended 
in  any  part  of  a circuit  is  found  by  multiply- 
ing the  current  in  amperes  flowing  through 
that  part  of  the  circuit  by  the  difference  in 
potential  between  its  terminals;  that  is, 
W=IE.  Using  Ohm’s  law  equation,  two 
more  formulas  may  be  derived  to  express  the 
energy  of  an  electric  circuit ; namely, 
W=E2/R  and  W=T2R.  To  obtain  experi- 
mentally the  energy  expended  in  an  arc  lamp 
circuit,  connect  it  up  through  a rheostat  to 
such  a line  voltage  as  the  instructor  indi- 
cates. Also  connect  a suitable  ammeter  and 
a voltmeter  to  this  circuit  under  the  direc- 
tions of  the  instructor.  When  the  resistance 
in  the  rheostat  is  about  half  on,  close  the  cir- 
cuit and  read  the  instruments  to  the  smallest 
possible  division.  Record  all  values  in  a 
suitable  table. 

Move  the  regulator  on  the  rheostat  so  that 
you  will  have  less  resistance  in  the  circuit. 
Note  the  effect  of  this  on  the  reading  of  the 
instruments  and  record  these  results. 

1.  What  would  happen  if  the  carbons  were 
left  in  contact? 

2.  Is  alternating  current  ever  used  on  an 
arc  lamp? 

3.  What  arrangement  is  made  to  feed  the 
carbons  on  a street  arc  lamp? 

4.  How  could  you  determine  which  carbon 
is  positive? 

From  a previous  experiment,  enter  in  the 


tabular  form  the  values  called  for  opposite 
each  of  the  lamps  or  lamp  combinations  nam- 
ed. By  means  of  the  three  formulas,  calcu- 
late the  energy  consumed  in  each  case. 

5.  Do  all  three  results  agree? 


Circuit  in  which  thel 

1 E5I 

energy  is  to  be  meas-l  I 

E 

R 

W=IE|\V=—  W = I2I 

ured  1 

1 R 1 

Arc  Lamp,  1st  Trial.... 

Arc  Lamp,  2nd  Trial.. 

One  incandescent  lamp 

Two  lamps  in  parallel.. 

Three  lamps  in  parallel 

PROBLEM  No.  58 


To  Determine  the  Cost  Per  Hour  of  Operating  an  Electric  Flatiron  and  an  Electric 

Toaster,  Etc. 

Directions:  In  connecting  a voltmeter 
and  an  ammeter  to  a 110-volt  service  line  of 
direct  current,  care  must  be  taken  that  the 
positive  terminals  of  the  instruments  be  con- 
nected to  the  positive  side  of  the  line.  To 
find  the  direction  of  the  flow  of  current  in 
the  line,  use  a voltmeter  with  the  binding 
posts  marked  plus  and  minus,  or  connect  the 
wires  to  a lamp  (110  volt),  (never  touch  the 
wires  together),  recall  the  thumb  rule  and, 
with  the  aid  of  a compass,  apply  the  rule. 

Having  determined  the  positive  side  of  the 
service  line,  connect  the  flatiron  in  series  with 
the  ammeter  and  connect  the  voltmeter 
across  the  line.  While  making  the  connec- 
tions, be  sure  that  the  current  is  “off.”  Do 
not  turn  the  current  on  until  the  instructor 
has  O.K.d  the  connections. 

Take  readings  of  the  two  instruments 
every  minute  for  five  minutes,  average  and 
place  them  in  the  following  chart.  Use  cur- 
rent rates  in  computing  the  cost. 

Next,  put  the  toaster  in  the  circuit  and  do 
a?  directed  for  the  iron. 


Device 

Volts 

Watts 

Rate 

Per  Kw. 

Cost  per  Hour 
of  Operation 

Toaster 

Flatiron 

1.  Sketch  the  connections  and  tell  what 
was  done. 

2.  I find  the  cost  to  operate  an  electric  flat- 
iron each  hour  to  be  cents  and  a 

toaster  to  be cents. 

8.  What  would  it  cost  to  burn  the  lights 
in  your  laboratory  for  a double  period,  using 
the  Minneapolis  rate  as  a basis? 

4.  What  would  it  cost  to  operate  a 110  volt 
1.5  ampere  Christmas  tree  lighting  outfit  one 
week,  three  hours  per  night,  if  electricity 
costs  10  cents  per  Kw.  hour? 

5.  If  it  takes  40  amperes  of  current  at  110 
volts  to  run  the  light  of  a moving  picture 
machine,  what  would  it  cost  to  keep  this  light 
burning  for  two  hours  at  current  rates? 


) 


PROBLEM  No.  59 


i 


To  Find  the  Per  Cent  of  Total  Electrical  Energy  Which  Is  Turned  Into  Useful  Heat  En- 
ergy in  an  Electric  Disc  Stove,  Immersion  Heater,  Etc. 

3 

Connect  up  a disc  stove  in  circuit  with  a 
suitable  ammeter  in  series  and  a voltmeter 
across  the  circuit.  Let  the  water  in  the  fau- 
cet run  until  it  is  as  cold  as  it  will  get,  then 
carefully  weigh  out  about  500  grams  of  it  in 
a calorimeter.  Place  the  calorimeter  on  the 
stove  and  take  the  temperature  of  the  water. 

Also  note  the  room  temperature  and  calcu- 
late the  temperature  to  which  the  water  must  ; 
be  heated  so  that  it  will  finally  be  as  much 
above  the  room  temperature  as  it  is  below  in 
the  beginning. 

After  the  circuit  has  been  O.K.d  by  the  in- 
structor, note  the  time  to  seconds,  close  the 
circuit,  read  the  ammeter  and  voltmeter  and 
constantly  stirring  the  water  with  the  ther- 
mometer, let  it  attain  the  desired  tempera- 
ture above  the  room  temperature  as  comput- 
ed above.  If  there  is  considerable  variation 
in  the  ammeter  and  voltmeter  readings  as 
the  heating  continues,  read  them  every  min- 
ute and  finally  average  the  separate  readings. 

Take  the  time  when  the  water  reaches  the 
desired  temperature,  and  calculate  the  time 
elapsed  in  seconds. 

Compute  the  resistance  of  the  stove  and 
the  calories  of  heat  gained  by  the  water.  Al- 
so compute  the  total  energy  supplied  by  the 
formula,  H equals  .24  I2Rt,  as  explained  in 
your  text.  Divide  the  calories  gained  by  the 
water  by  the  calories  given  off  by  the  current. 

Repeat  the  experiment  with  an  immersion 
heater  and  any  other  heating  device  you  may 
have  time  for.  Record  all  readings  and  com- 
putations in  a neat  form. 

1.  What  becomes  of  the  wasted  energy? 

2.  Which  device  has  the  highest  efficiency 
and  why? 

3.  Give  any  conditions  under  which  less 
energy  would  be  wasted  in  any  of  the  cases. 


PROBLEM  No.  60 


To  Find  the  Cost  of  Bringing  a Pint  of  Water  to  the  Boiling  Point  On  An  Ordinary  Gas 
Burner  and  Compute  the  Efficiency  of  the  Burner  and  Kettle. 


Weigh  carefully  a pound  of  water  in  an  or- 
dinary pan  or  kettle.  (A  pound  is  practic- 
ally a pint.)  Use  the  gas  meter  provided  un- 
der the  directions  of  the  instructor.  Take 
the  temperature  of  the  water,  then  place  it 
upon  the  gas  burner  covered,  turn  on  the  gas 
from  the  meter,  and  allow  the  gas  to  burn 
until  the  water  begins  to  boil.  (Do  not  mis- 
take air  bubbles  for  boiling.)  Read  the  dial 
on  the  scale  when  boiling  begins  and  take  the 
temperature  of  the  water.  At  current  price, 
compute  the  cost  of  that  used  in  boiling  the 
pint  of  water. 

To  compute  the  efficiency,  find  the  number 
of  B.T.U.  used  up  by  allowing  600  B.T.U.  for 
each  cu.  ft.  of  gas;  find  the  B.T.U.  turned 
into  useful  heat  by  multiplying  the  weight  of 
the  water  by  the  number  of  degrees  Fahren- 
heit raised.  Divide  the  number  of  B.T.U., 
which  are  useful,  by  the  total  number  used 
and  the  result  is  efficiency. 

1.  Mention  ways  in  which  the  efficiency 
could  be  increased. 

, 2.  At  this  rate,  calculate  the  cost  of  heat- 
ing the  water  in  a 20  gallon  tank  from  50°  F. 
to  212°  F. 

3.  How  does  the  efficiency  of  electric  burn- 
ers compare  with  that  of  gas  burners? 


■ 

■ 

■ 

. 

' 

“ . , , 

( 


PROBLEM  No.  61 


To  Diagram  and  Explain  the  Acttion  of  a Telephone. 

I.  Trace  out  the  complete  circuit  of  a tele- 
phone line  between  two  points.  Represent 
your  findings  in  a diagram  with  a complete 
instrument  at  each  point. 


1.  Will  the  bell  ring  when  the  receiver  is 
on  the  hook?  Trace  the  circuit  on  your  dia- 
gram to  answer  this  question. 

With  the  receiver  off  the  hook,  trace  the 
circuit  through  the  transmitter  and  the  pri- 
mary coil..  .2.  Is  it  complete? 

3.  What  change  takes  place  in  the  connec- 
tions with  the  receiver  on  and  off  the  hook? 

4.  Explain  the  action  of  a telephone  in 
transmitting  sounds. 

II.  Study  the  construction  and  action  of 
a microphone.  This  instrument  was  very 
closely  connected  with  the  early  history  of 
the  telephone.  Listen  to  the  sounds  of  a 
watch  lying  on  the  microphone.  1.  Is  the 
reproduction  like  the  original  sound  in  char- 
acter? 2.  Is  it  louder?  3.  Diagram  the 
microphone  circuit. 


>V.  ' , 


' • 


PROBLEM  No.  62 


To  Study  the  Motor  and  Dynamo. 

Simple  motors  and  dynamos  are  alike  in  j 
construction.  Some  companies  make  a ma-  j 
chine  which  can  be  used  either  as  a motor  or  j 
as  a dynamo.  If  a machine  is  to  be  used  as 
a dynamo,  the  core  of  the  field  magnets  must 
be  made  of  hard  enough  iron  to  retain  suffi- 
cient magnetism  to  furnish  a weak  field ; oth- 
erwise there  will  be  no  currnt  produced  when 
the  armature  is  rotated.  With  the  machine 
used  as  a motor,  on  the  other  hand,  it  is  not 
necessary  that  the  cores  of  the  field  magnets 
retain  any  magnetism.  The  St.  Louis  mo- 
tors to  be  used  in  this  experiment  will,  with 
the  bar  magnets,  serve  either  as  motors  or 
dynamos,  though  there  is  no  arrangement 
made  to  rotate  the  armature  as  a dynamo. 

Use  a St.  Louis  motor  with  the  bar  mag-  ! 
nets  in  position.  (Be  sure  that  opposite 
poles  are  on  either  side  of  the  armature.)  In 
order  to  produce  rotation  when  the  current  is 
turned  on,  the  brushes  must  be  in  the  proper 
position.  Study  the  instrument  and  deter- 
mine where  the  armature  should  be  when 
the  current  changes  direction  so  that  it  con- 
tinue its  rotation.  Adjust  the  brushes  so 
that  the  change  of  current  will  come  at  the 
proper  place.  Connect  the  instrument  with 
a dry  cell.  If  the  brushes  have  been  ad- 
justed correctly,  the  armature  will  rotate. 

1.  In  what  position  did  you  determine  the 
aramture  should  be  when  the  current 
changes  direction? 

2.  Did  you  have  any  trouble  in  making  the 
armature  rotate?  If  so,  what?  Attach  the 
wires  so  that  the  current  will  flow  through 
the  motor  in  an  opposite  direction  and  note 
the  direction  of  rotation  as  compared  with 
that  at  first. 

3.  What  is  the  direction  of  rotation  as 
compared  with  that  at  first? 

(Reverse  the  magnets.) 

4.  What  is  the  effect  on  the  direction  of 
rotation  ? 

With  the  armature  rotating,  gradually 
move  the  bar  magnets  away. 

5.  What  is  the  effect?  Why? 

Attach  the  electromagnet  so  that  the  cur- 
rent on  entering  will  divide,  part  passing 
through  the  armature  and  part  through  the 


field  magnets.  This  is  called  a shunt  wind-  I 
ing.  See  that  the  brushes  are  adjusted  cor- 
rectly so  that  the  motor  will  operate. 

6.  Does  the  speed  of  rotation  seem  to  be 
slower  or  faster  than  with  the  bar  magnets  ? 

(Change  the  direction  of  the  current 
through  the  instrument.) 

7.  Does  this  affect  the  direction  of  rota- 
tion? 

(Arrange  the  wires  so  that  all  the  current 
must  pass  through  both  the  field  magnet  and 
armature.  This  is  called  a series  winding.) 

8.  Does  the  armature  rotate  as  fast  as 
with  the  shunt  winding? 

(Reverse  the  current.) 

9.  Does  this  affect  the  direction  of  rota- 
tion? 

Disconnect  the  dry  cell  and  replace  the  bar 
magnets.  Attach  a D’Arsonva!  galvanomet- 
er to  the  terminals  and  spin  the  armature, 
first  in  one  direction  and  then  in  the  opposite 
direction. 

10.  What  was  the  direction  of  the  current 
in  the  second  case  as  compared  with  the  first, 
as  shown  by  the  galvanometer  needle? 

11.  What  factors  affect  the  voltage  of  a 
dynamo  ? 


PROBLEM  No.  63 


To  Find  the  Efficiency  of  an  Electric  Motor. 

Use  the  electric  motor  furnished.  Con- 
nect a suitable  voltmeter  across  the  terminals 
of  the  motor  and  a suitable  ammeter  in  series 
with  it.  See  diagram  or  model.  (Be  sure 
you  are  using  the  proper  instruments  and 
that  they  are  connected  up  correctly  by  con- 
sulting with  the  instructor  before  the  current 
is  turned  on.)  The  motor  should  be  “braked” 
by  a small  belt  or  cord  fastened  to  two  draw 
scales,  as  shown  in  the  diagram  or  model. 

With  the  motor  running,  read  the  volt- 
meter and  ammeter  and  the  two  spring  bal- 
ances. Also,  using  a speed  counter,  count 
the  number  of  revolutions  per  minute,  and 
measure  the  circumference  of  the  pulley 
around  which  the  cord  passes.  Watts  put-in 
equals  volts  times  amperes,  and  watts  got- 
ten out  equals  load  in  kg.  (difference  in  the 
reading  of  balances)  times  circumference  of 
pulley,  times  revolutions  per  minute  divided 
by  6.12  (the  number  of  kg.  meters  per  min- 
ute equivalent  to  1 watt). 

Make  three  trials  with  different  brake 
loads  and  tabulate  as  follows: 

12  3 

1.  Reading  of  voltmeter 

2.  Reading  of  ammeter 

3.  Watts  (input)  VxA — 

4.  Reading  of  Balance  A 

5.  Reading  of  Balance  B 

6.  Load  in  Kg.  (differ- 

ence in  readings) 

7.  Circumference  of 

pulley  

8.  Rotations  per  minute 

9.  Work  done  per 

minute  

10.  Watts — Output 

11.  Efficiency  (Output^- 

Input) 

A.  Find  the  H.P.  of  the  motor  above. 

B.  How  does  the  load  affect  the  efficiency? 

C.  How  does  the  load  affect  the  current 
needed  to  run  the  motor? 

D.  Find  the  cost  at  $0.10  per  K.W.  hour  to 
run  the  motor  under  the  heaviest  load  for  10 
hours. 


PROBLEM  No.  64 


To  Construct  a Small  Step-Down  Transformer. 


The  core  design  offered  will  be  found  serv- 
iceable up  to  about  600  watts.  By  the  use  of 
this  design,  form  wound  coils  may  be  used. 

This  form,  which  is  actual  size,  should  be 
built  up  to  7.6  cm.  in  thickness.  The  sheets 
should  be  about  .3  mm.  thick.  600  watts  on 
120  volts  would  require  5 amperes  primary. 
600  watts  at  40  volts  would  require  15  am- 
peres secondary.  (Consider  the  efficiency 
100  per  cent.) 

Wire  table  shows  No.  20  copper  will  carry 
5.7  amperes;  No.  14  copper  will  carry  16.2 
amperes.  Hence,  these  sizes  should  be  used. 
By  Ohm’s  law,  we  should  have  24  ohms  re- 
sistance in  the  primary.  It  has  been  found 
that  2.58  ohms  are  all  that  is  required.  The 
balance  is  made  up  by  the  A.C.  effect  known 
as  impedance.  By  consulting  the  wire  table, 
we  find  that  250  ft.  No.  20  will  give  2.58 
ohms.  The  number  of  turns  this  makes 
when  wound  into  the  primary  coil  enables  us 
to  determine  the  number  of  turns  required 
in  the  secondary.  Vp:Vs:  :Tp:Ts,  or 
120 :40 : :360 :120.  In  case  different  voltages 
are  required,  taps  should  be  brought  out  of 
the  secondary  at  points  so  that  the  ratio  of 
the  number  of  turns  in  the  primary  and  sec- 
ondary will  conform  to  the  voltage  ratio. 

The  insulation  between  the  primary  and 
core  must  be  constructed  with  great  care. 
Use  mica  wherever  possible  and  empire  cloth 
on  the  sharp  angles. 

When  the  insulation  has  been  completed, 
the  transformer  should  be  tested  for  voltage  j 


breakdown  by  subjecting  it  to  100%  over- 
voltage for  a few  moments.  Then  run  it  for 
an  hour  or  more  at  normal  voltage  and  note 
whether  it  heats  to  excess.  If  these  tests 
are  satisfactory,  the  transformer  should  be 
mounted  in  a sheet  iron  box  a little  larger 
than  the  transformer  itself.  The  space 
should  then  be  filled  with  insulating  com- 
pound, which  protects  the  coils  from  mechan- 
ical injury  and  the  insulation  from  moisture. 
The  primary  and  secondary  leads  should  have 
hard  rubber  bushings  where  they  pass 
through  the  iron  case. 

By  using  a large  number  of  turns  of  very 
fine  wire  in  the  secondary,  this  transformer 
may  be  used  as  a step-up  for  high  voltage. 


